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Smooth map which is a diffeomorphism upon restriction
injective open map. A local diffeomorphism has constant rank of n . {\displaystyle n.} A diffeomorphism is a bijective local diffeomorphism. A smooth covering
Local_diffeomorphism
Isomorphism of differentiable manifolds
A C 1 {\displaystyle C^{1}} -diffeomorphism is simply a diffeomorphism, and a C 0 {\displaystyle C^{0}} -diffeomorphism is a homeomorphism. Given a subset
Diffeomorphism
Definition of a class of dynamical systems
Anosov system. Let M be a smooth manifold with a diffeomorphism f: M→M. Then f is an axiom A diffeomorphism if the following two conditions hold: The nonwandering
Axiom_A
Mathematical function revertible near each point
about homeomorphic subsets of Euclidean space Local diffeomorphism – Smooth map which is a diffeomorphism upon restriction Locally Hausdorff space – Space
Local_homeomorphism
Map from a Lie algebra to its Lie group
be a local diffeomorphism at all points. For example, the exponential map from s o {\displaystyle {\mathfrak {so}}} (3) to SO(3) is not a local diffeomorphism;
Exponential_map_(Lie_theory)
Linear approximation of smooth maps on tangent spaces
need not be invertible. However, if φ {\displaystyle \varphi } is a local diffeomorphism, then d φ x {\displaystyle d\varphi _{x}} is invertible, and the
Pushforward_(differential)
No complete regular surface of constant negative gaussian curvature immerses in R3
S ) ⟶ S {\displaystyle \exp _{p}:T_{p}(S)\longrightarrow S} is a local diffeomorphism (in fact a covering map, by Cartan-Hadamard theorem), therefore,
Hilbert's theorem (differential geometry)
Hilbert's_theorem_(differential_geometry)
Diffeomorphism that has a hyperbolic structure on the tangent bundle
Bernoulli map, and Arnold's cat map. If the map is a diffeomorphism, then it is called an Anosov diffeomorphism. If a flow on a manifold splits the tangent bundle
Anosov_diffeomorphism
Distance-preserving mathematical transformation
{\displaystyle f} is a local diffeomorphism such that g = f ∗ g ′ , {\displaystyle g=f^{*}g',} then f {\displaystyle f} is called a local isometry. A collection
Isometry
Algebraic geometry
étale if it has a lifting property that is analogous to being a local diffeomorphism. Let A be a topological ring, and let B be a topological A-algebra
Formally_étale_morphism
Result in dynamical systems theory
roughly states that the existence of a local diffeomorphism near a fixed point implies the existence of a local stable center manifold containing that
Stable_manifold_theorem
Assignment of vector fields to manifolds
following: Theorem—If φ : M → N {\displaystyle \varphi :M\to N} is a local diffeomorphism at x {\displaystyle x} in M {\displaystyle M} , then d φ x : T x
Tangent_space
Map from tangent space to the manifold
exponential map is an embedding (i.e., the exponential map is a local diffeomorphism). The radius of the largest ball about the origin in TpM that can
Exponential map (Riemannian geometry)
Exponential_map_(Riemannian_geometry)
Differential geometry technique
up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, when is there a diffeomorphism ϕ : M →
Cartan's_equivalence_method
Branch of mathematics
of all smooth manifolds up to diffeomorphism. Since dimension is an invariant of smooth manifolds up to diffeomorphism type, this classification is often
Differential_topology
System in control theory
transformation H ( x ) {\displaystyle H(x)} is guaranteed to be a local diffeomorphism. The diagonal matrix M ( x ^ ) {\displaystyle M({\hat {x}})} of gains
State_observer
Nonlinear differential operator used to study conformal mappings
interpreted as a continuous 1-cocycle or crossed homomorphism of the diffeomorphism group of the circle with coefficients in the module of densities of
Schwarzian_derivative
Theorem in mathematics
of F is an isomorphism at all points p in M then the map F is a local diffeomorphism. The inverse function theorem can also be generalized to differentiable
Inverse_function_theorem
Principle stating that physical laws are the same in all coordinate systems
In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical
General_covariance
Vector field
a vector field on M. Then X generates a one-parameter group of local diffeomorphisms FlXt, the flow along X. The differential of FlXt gives, for each
Variational_vector_field
Feature of a system that is preserved under some transformation
as the general field h ( x ) {\displaystyle h(x)} (also known as a diffeomorphism) has the infinitesimal effect on a scalar ϕ ( x ) {\displaystyle \phi
Symmetry_(physics)
Mathematical operation on invertible matrices
{\displaystyle {\mathfrak {g}}} . Note that the exponential map is a local diffeomorphism between a neighborhood U {\displaystyle U} of the zero matrix 0 _
Logarithm_of_a_matrix
rank f = dim N (i.e. the derivative is everywhere surjective), a local diffeomorphism if rank f = dim M = dim N (i.e. the derivative is everywhere bijective)
Rank_(differential_topology)
Concept in topology
regular value, in a neighborhood of each xi the map f is a local diffeomorphism. Diffeomorphisms can be either orientation preserving or orientation reversing
Degree of a continuous mapping
Degree_of_a_continuous_mapping
Operation in differential geometry
neighborhood U of p. Abusing notation slightly, we may regard (xi) as a local diffeomorphism ( x i ) : M → R n {\displaystyle (x^{i}):M\rightarrow \mathbb {R}
Jet_(mathematics)
Concept in algebraic geometry
is a local diffeomorphism, i.e. for any point y ∈ Y, there is an open neighborhood U of x such that the restriction of f to U is a diffeomorphism. This
Étale_morphism
Type of derivative in differential geometry
one-dimensional groups of diffeomorphisms) on M, the Lie derivative is the differential of the representation of the diffeomorphism group on tensor fields
Lie_derivative
Lie group homomorphism from the real numbers
induces a local flow - a one parameter group of local diffeomorphisms, sending points along integral curves of the vector field. The local flow of a vector
One-parameter_group
Inclusion of one mathematical structure in another, preserving properties of interest
injective function is locally injective but not conversely. Local diffeomorphisms, local homeomorphisms, and smooth immersions are all locally injective
Embedding
Locally metrizable Given some notion of equivalence (e.g., homeomorphism, diffeomorphism, isometry) between topological spaces, two spaces are said to be locally
Local_property
Mathematics of smooth surfaces
gives a diffeomorphism between a disc ‖v‖ < δ and a neighbourhood of p; more generally the map sending (p, v) to expp(v) gives a local diffeomorphism onto
Differential geometry of surfaces
Differential_geometry_of_surfaces
Internal groupoid in the category of smooth manifolds
{\displaystyle G} and M {\displaystyle M} are equal; s {\displaystyle s} is a local diffeomorphism; all the s {\displaystyle s} -fibres are discrete As a consequence
Lie_groupoid
Study of angle-preserving transformations of a geometric space
a Möbius geometry, meaning that there exists an angle-preserving local diffeomorphism from the manifold into a Möbius geometry. In two dimensions, every
Conformal_geometry
Branch of geometry
geometry is a stable distribution, since they are all the same up to local diffeomorphism. α {\displaystyle \alpha } does not need to be globally defined.
Contact_geometry
Algebraic object with geometric applications
transformations (or, other transformations within some class, such as local diffeomorphisms). This makes a tensor a special case of a geometrical object, in
Tensor
Differentiable function whose derivative is everywhere injective
p. 243, Spivak 1999, p. 46. This kind of definition, based on local diffeomorphisms, is given by Bishop & Goldberg 1968, p. 40, Lang 1999, p. 26. This
Immersion_(mathematics)
Construction in differential topology
canonical diffeomorphism between the first jet bundle J 1 ( π ) {\displaystyle J^{1}(\pi )} and T*M × R. To construct this diffeomorphism, for each σ
Jet_bundle
Concept in mathematics
function Smooth morphism Étale morphisms – The algebraic analogue of local diffeomorphisms. Resolution of singularities contraction morphism Here is the argument
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
Differential map between manifolds whose differential is everywhere surjective
{R} ^{m+n}\rightarrow \mathbb {R} ^{n}\subset \mathbb {R} ^{m+n}} Local diffeomorphisms Riemannian submersions The projection in a smooth vector bundle
Submersion_(mathematics)
Function in mathematics
field on R2 uniquely determined by v (since the pushforward of a local diffeomorphism at any point is invertible). Furthermore, on the overlap between
Connection_(mathematics)
Field equation from quantum gravity
commutation relations with the diffeomorphism constraints generate the Bergman–Komar "group" (which is the diffeomorphism group on-shell). In canonical
Wheeler–DeWitt_equation
Representation theory of the symmetries of manifolds
orientation-preserving diffeomorphism group of M (only the identity component of mappings homotopic to the identity diffeomorphism if you wish) and Diffx1(M)
Representation theory of diffeomorphism groups
Representation_theory_of_diffeomorphism_groups
n-sphere. The development of a conformally flat manifold is a conformal local diffeomorphism from the universal cover of the manifold to the n-sphere. The class
Development (differential geometry)
Development_(differential_geometry)
{\displaystyle x} of radius r . {\displaystyle r.} One then defines a diffeomorphism f : B r ( x ) → B r ( y ) {\displaystyle f:B_{r}(x)\rightarrow B_{r}(y)}
Cartan–Ambrose–Hicks_theorem
Mathematical operation
ϕ {\displaystyle \phi } . When the map ϕ {\displaystyle \phi } is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform
Pullback (differential geometry)
Pullback_(differential_geometry)
that f ( p , ⋅ ) : M → N {\displaystyle f(p,\cdot ):M\to N} is a local diffeomorphism for every p ∈ P {\displaystyle p\in P} , then the function P × F
Natural_bundle
linear mapping of vector bundles. The problem is invariant under local diffeomorphism, so it is sufficient to prove it when M is an open set in Rn and
Peetre_theorem
to local diffeomorphism, the affine focal set. If the family of affine distance functions can be shown to be a certain kind of family then the local structure
Affine_focal_set
Generalized manifold
3-manifold. Let φ be a non-trivial periodic orientation-preserving diffeomorphism of M. Then M admits a φ-invariant hyperbolic or Seifert fibered structure
Orbifold
3-sphere (or (2n + 1)-sphere) by a free isometric action of Z – k. Local diffeomorphism Manifold – A topological manifold is a locally Euclidean Hausdorff
Glossary of differential geometry and topology
Glossary_of_differential_geometry_and_topology
Physical theory with fields invariant under the action of local "gauge" Lie groups
system can be chosen freely under arbitrary diffeomorphisms of spacetime. Both gauge invariance and diffeomorphism invariance reflect a redundancy in the description
Gauge_theory
Generalization of a foliation
every x ∈ U α ∩ U β {\displaystyle x\in U_{\alpha }\cap U_{\beta }} , a diffeomorphism ψ α β x {\displaystyle \psi _{\alpha \beta }^{x}} between open neighbourhoods
Haefliger_structure
Concept in differential geometry
plot of the first space is a plot of the second space. It is called a diffeomorphism if it is smooth, bijective, and its inverse is also smooth. Equipping
Diffeology
Continuous surjection satisfying a local triviality condition
morphisms. Or is, at least, invertible in the appropriate category; e.g., a diffeomorphism. Steenrod, Norman (1951), The Topology of Fibre Bundles, Princeton University
Fiber_bundle
Smooth manifold that is homeomorphic but not diffeomorphic to a sphere
structures on the 7-sphere. In any dimension Milnor (1959) showed that the diffeomorphism classes of oriented exotic spheres form the non-trivial elements of
Exotic_sphere
Isomorphism of symplectic manifolds
structure of phase space, and is called a canonical transformation. A diffeomorphism between two symplectic manifolds f : ( M , ω ) → ( N , ω ′ ) {\displaystyle
Symplectomorphism
Concept in mathematics
imposes several conditions on sets of homeomorphisms (respectively, diffeomorphisms) defined on open sets U of a given Euclidean space or more generally
Pseudogroup
Mathematical problem concerning limit cycles in dynamical systems
; Yakovenko, S. (1991). "Finitely-smooth normal forms of local families of diffeomorphisms and vector fields". Russian Mathematical Surveys, 46(1), 3–39
Hilbert–Arnold_problem
Trick relating differential forms
_{0}} and α 1 {\displaystyle \alpha _{1}} on a smooth manifold by a diffeomorphism ψ ∈ D i f f ( M ) {\displaystyle \psi \in \mathrm {Diff} (M)} such that
Moser's_trick
Two-dimensional manifold
higher-dimensional manifolds.) Thus closed surfaces are classified up to diffeomorphism by their Euler characteristic and orientability. Smooth surfaces equipped
Surface_(topology)
Way to join two given mathematical manifolds together
then the result is unique up to diffeomorphism. There are subtle problems in the smooth case: not every diffeomorphism between the boundaries of the spheres
Connected_sum
Facet of general relativity
translations is finite-dimensional. Because general relativity is a diffeomorphism invariant theory, it has an infinite continuous group of symmetries
Mass_in_general_relativity
f is called an Anosov diffeomorphism. The dynamics of f on a hyperbolic set, or hyperbolic dynamics, exhibits features of local structural stability and
Hyperbolic_set
Super vector space forming base superspace for supersymmetric field theories
theory. But these generate local diffeomorphisms, which is a signature of gravitational theories. So any theory with local supersymmetry is necessarily
Super_Minkowski_space
Motion of particles in a fluid
one-parameter group of homeomorphisms and diffeomorphisms, respectively. In certain situations one might also consider local flows, which are defined only in some
Flow_(mathematics)
Mathematical behavior near singularities
consider its induced diffeomorphism on local transversal sections through the endpoints. Within a simply connected chart this diffeomorphism becomes unique
Monodromy
Type of symmetry in physics
whose local flow diffeomorphisms preserve some property of the spacetime. (Note that one should emphasize in one's thinking this is a diffeomorphism—a transformation
Spacetime_symmetries
Group that is also a differentiable manifold with group operations that are smooth
whose inverse is also a Lie group homomorphism. Equivalently, it is a diffeomorphism which is also a group homomorphism. Observe that, by the above, a continuous
Lie_group
Interdisciplinary field of biology
more general diffeomorphism group has been the group of choice, which is the infinite dimensional analogue. The high-dimensional diffeomorphism groups used
Computational_anatomy
Theorem in hyperbolic geometry
{\displaystyle 6g-6} that parameterizes all metrics of constant curvature (up to diffeomorphism), a fact essential for Teichmüller theory. There is also a rich theory
Mostow_rigidity_theorem
Theory of quantum gravity merging quantum mechanics and general relativity
spatial diffeomorphism on γ {\displaystyle \gamma } instead. Therefore, the meaning of O ^ ′ {\displaystyle {\hat {O}}'} is a spatial diffeomorphism on γ
Loop_quantum_gravity
Special coordinate system in differential geometry
neighborhood V of the origin in the tangent space TpM, and expp acts as a diffeomorphism between U and V. On a normal neighborhood U of p in M, the chart is
Normal_coordinates
Tangent spaces of a manifold
{\displaystyle \phi _{\alpha }:U_{\alpha }\to \mathbb {R} ^{n}} is a diffeomorphism. These local coordinates on U α {\displaystyle U_{\alpha }} give rise to an
Tangent_bundle
Conditions under which a chaotic system can be reconstructed by observation
space with k > 2 d A . {\displaystyle k>2d_{A}.} That is, there is a diffeomorphism φ that maps A into R k {\displaystyle \mathbb {R} ^{k}} such that the
Takens's_theorem
Topological space that locally resembles Euclidean space
manifold. Similarly, for a differentiable manifold, it has to be a diffeomorphism. For other manifolds, other structures should be preserved. A finite
Manifold
Key constraint in some theories admitting Hamiltonian formulations
constraint technically refers to a linear combination of spatial and time diffeomorphism constraints reflecting the reparametrizability of the theory under both
Hamiltonian_constraint
Rate of separation of infinitesimally close trajectories
trajectory and the Lyapunov dimension of attractor are invariant under diffeomorphism of the phase space. The multiplicative inverse of the largest Lyapunov
Lyapunov_exponent
Philosophical argument against general covariance
a diffeomorphism, sometimes called an active diffeomorphism by physicists to distinguish it from coordinate transformations (passive diffeomorphisms).
Hole_argument
Smooth manifold with an inner product on each tangent space
map f : M → N , {\displaystyle f:M\to N,} not assumed to be a diffeomorphism, is a local isometry if every p ∈ M {\displaystyle p\in M} has an open neighborhood
Riemannian_manifold
Manifold upon which it is possible to perform calculus
of higher-order jets. Define a k-th order frame to be the k-jet of a diffeomorphism from Rn to M. The collection of all k-th order frames, Fk(M), is a principal
Differentiable_manifold
Diagram used to represent quantum field theory calculations
exact duality over a lattice. Over a manifold however, assumptions like diffeomorphism invariance are needed to make the duality exact (smearing Wilson loops
Spin_network
Description of gauge theories using loop operators
spatial diffeomorphism invariance of general relativity. The loop representation also provides a natural solution of the spatial diffeomorphism constraint
Loop representation in gauge theories and quantum gravity
Loop_representation_in_gauge_theories_and_quantum_gravity
Subset of a manifold that is a manifold itself; an injective immersion into a manifold
{\displaystyle S} is a manifold and the inclusion f {\displaystyle f} is a diffeomorphism: this is just the topology on N {\displaystyle N} , which in general
Submanifold
Mathematics award
US "Major contributions in the primes, in univalent functions and the local Bieberbach conjecture, in theory of functions of several complex variables
Fields_Medal
Mapping which preserves all topological properties of a given space
the homeomorphism from X to Y. Local homeomorphism – Mathematical function revertible near each point Diffeomorphism – Isomorphism of differentiable
Homeomorphism
Statistical model used in machine learning
invertible (more specifically it is a bijection and a homeomorphism and a diffeomorphism), with inverse f lin ( ⋅ ; M − 1 ) {\displaystyle f_{\text{lin}}(\cdot
Flow-based_generative_model
Point on a curve where motion must move backwards
differentiable functions: a curve has a cusp at a point if there is a diffeomorphism of a neighborhood of the point in the ambient space, which maps the
Cusp_(singularity)
Result of differential geometry proved by Gauss
{\displaystyle \mathbf {r} _{vu}=\mathbf {r} _{uv}} .) Definition: A diffeomorphism ϕ : S → S ~ {\displaystyle \phi :S\to {\tilde {S}}} is an isometry if
Theorema_Egregium
Algebraic structure used in analysis
Lie algebra of the diffeomorphism group of X. So the Lie bracket of vector fields describes the non-commutativity of the diffeomorphism group. An action
Lie_algebra
f^{-1}(U)\cong X_{0}\times U\twoheadrightarrow X_{0}} is a diffeomorphism. This diffeomorphism is not unique because it depends on the choice of trivialization
Period_mapping
2D conformal field theory used in string theory
^{2}\right).\end{aligned}}} The action is invariant under worldsheet diffeomorphisms (or coordinates transformations) and Weyl transformations. Assume the
Polyakov_action
Extension of quantum field theory to curved spacetime
invariant under diffeomorphisms. If t ′ ( t ) {\displaystyle t'(t)} is a diffeomorphism, then, in general, the Fourier transform of e i k t ′ ( t ) {\displaystyle
Quantum field theory in curved spacetime
Quantum_field_theory_in_curved_spacetime
Theoretical framework in physics
according to the geometry (local structure) of the spacetime background, while TQFTs are invariant under spacetime diffeomorphisms but are sensitive to the
Quantum_field_theory
Type of map used in mathematics, particularly dynamical systems
point p if P(p) = p P(U) is a neighborhood of p and P:U → P(U) is a diffeomorphism for every point x in U, the positive semi-orbit of x intersects S for
Poincaré_map
Mathematical model of the time dependence of a point in space
{\mathcal {T}}} into the space of diffeomorphisms of the manifold to itself. In other terms, f(t) is a diffeomorphism, for every time t in the domain T
Dynamical_system
Suite of algorithms
a variational problem in which the template is transformed via the diffeomorphism used as a change of coordinate to minimize a squared-error matching
Large deformation diffeomorphic metric mapping
Large_deformation_diffeomorphic_metric_mapping
Griffin, Ken Ono, 2015) Anderson conjecture on the finite number of diffeomorphism classes of the collection of 4-manifolds satisfying certain properties
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Branch of differential geometry
theorem. Given constants C, D and V, there are only finitely many (up to diffeomorphism) compact n-dimensional Riemannian manifolds with sectional curvature
Riemannian_geometry
Bijection of a set using properties of shapes in space
refined. Conformal transformation Equiareal transformation Homeomorphism Diffeomorphism Transformations of the same type form groups that may be sub-groups
Geometric_transformation
Key result in general relativity
Suppose that K is an open precompact subset of M such that there is a diffeomorphism Φ : ℝ3 − B1(0) → M − K, and suppose that there is a number m such that
Positive_energy_theorem
LOCAL DIFFEOMORPHISM
LOCAL DIFFEOMORPHISM
Boy/Male
British, English
Loyal
Boy/Male
Irish American Welsh
Loyal.
Boy/Male
American, Australian, British, English, French
Faithful; True
Boy/Male
British, English
Loyal
Boy/Male
English American
Loyal.
Boy/Male
American, British, English
Loyal
Boy/Male
Irish Welsh
Loyal.
Boy/Male
Irish
Loyal.
Boy/Male
British, English
Loyal
Boy/Male
Indian
Loyal
Boy/Male
Arabic
Loyal
Girl/Female
Muslim
Loyal
Boy/Male
Irish
Loyal.
Boy/Male
Italian Greek
Loyal.
Boy/Male
English American French
Faithful; unswerving.
Girl/Female
French
Loyal.
Boy/Male
Irish Welsh
Loyal.
Boy/Male
American, British, English, Italian
Loyal
Girl/Female
Indian
Loyal
Girl/Female
Arabic, Muslim
Loyal
LOCAL DIFFEOMORPHISM
LOCAL DIFFEOMORPHISM
Boy/Male
Hindu, Indian, Kannada, Marathi, Oriya, Sanskrit, Telugu
Name of a King
Male
Norse
 Old Norse name composed of the name of the god Thor and the word ketill "cauldron," hence "Þórr's cauldron."
Boy/Male
Arabic, Muslim
Amazing; Handsome; Caring; Kind Hearted
Male
Vietnamese
Vietnamese name VÄ‚N means "cloud" or "male."
Male
Hebrew
(בְּתוּ×ֵל) Hebrew name BETHUW'EL means "God destroys" or "man of God." In the bible, this is the name of a town and also the name of the father of Rebecca.
Boy/Male
Hindu
Delight, Lord of all abodes
Girl/Female
American, Anglo, Australian, British, Christian, Danish, Dutch, English, French, German, Hawaiian, Hebrew, Irish, Italian, Jamaican, Portuguese
God is My Oath; My God is Bountiful; God of Plenty
Girl/Female
Hindu, Indian, Marathi
Joyous Girl
Male
French
Norman French name derived from Latin Alvinius, ALVIN means "elf friend."
Surname or Lastname
English
English : variant spelling of Son.Jewish (Ashkenazic) : variant of Sonne.
LOCAL DIFFEOMORPHISM
LOCAL DIFFEOMORPHISM
LOCAL DIFFEOMORPHISM
LOCAL DIFFEOMORPHISM
LOCAL DIFFEOMORPHISM
n.
Vocal expression; articulation; speech.
n.
A district or local division, as of a province.
a.
Of or pertaining to a vowel; having the character of a vowel; vowel.
n.
A local name of the burbot.
n.
A man who has a right to vote in certain elections.
a.
Alt. of Loral
a.
Consisting of, or characterized by, voice, or tone produced in the larynx, which may be modified, either by resonance, as in the case of the vowels, or by obstructive action, as in certain consonants, such as v, l, etc., or by both, as in the nasals m, n, ng; sonant; intonated; voiced. See Voice, and Vowel, also Guide to Pronunciation, // 199-202.
n.
A local European measure of length. See Canna.
n.
A vocal sound; specifically, a purely vocal element of speech, unmodified except by resonance; a vowel or a diphthong; a tonic element; a tonic; -- distinguished from a subvocal, and a nonvocal.
a.
Of or pertaining to a particular place, or to a definite region or portion of space; restricted to one place or region; as, a local custom.
a.
Belonging to,or concerning, a focus; as, a focal point.
n.
A train which receives and deposits passengers or freight along the line of the road; a train for the accommodation of a certain district.
a.
Loyal.
a.
Faithful; loyal.
a.
Faithful; loyal; true.
n.
A principle, practice, form of speech, or other thing of local use, or limited to a locality.
n.
On newspaper cant, an item of news relating to the place where the paper is published.
v. t.
To divide according to gepgraphical sections or local interests.
a.
Uttered or modulated by the voice; oral; as, vocal melody; vocal prayer.
a.
Confined to no zone or region; not local.