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Topics referred to by the same term
the connectedness theorem may be one of Deligne's connectedness theorem Fulton–Hansen connectedness theorem Grothendieck's connectedness theorem Hartshorne's
Connectedness_theorem
mathematics, Grothendieck's connectedness theorem, states that if A is a complete Noetherian local ring whose spectrum is k-connected and f is in the maximal
Grothendieck's connectedness theorem
Grothendieck's_connectedness_theorem
Zariski's connectedness theorem (due to Oscar Zariski) says that under certain conditions the fibers of a morphism of varieties are connected. It is an
Zariski's connectedness theorem
Zariski's_connectedness_theorem
Theorem of algebraic geometry and commutative algebra
is the special case of Zariski's connectedness theorem when the two varieties are birational. Zariski's main theorem can be stated in several ways which
Zariski's_main_theorem
Basic concept of graph theory
edge-connectivities of a disconnected graph are both 0. 1-connectedness is equivalent to connectedness for graphs of at least two vertices. The complete graph
Connectivity_(graph_theory)
Topological space that is connected
{\displaystyle \mathbb {C} ^{n}} are connected if and only if they are path-connected. Additionally, connectedness and path-connectedness are the same for finite topological
Connected_space
In mathematics, the Fulton–Hansen connectedness theorem is a result from intersection theory in algebraic geometry, for the case of subvarieties of projective
Fulton–Hansen connectedness theorem
Fulton–Hansen_connectedness_theorem
Path in a graph that visits each vertex exactly once
is n or greater. The following theorems can be regarded as directed versions: Ghouila–Houiri (1960)—A strongly connected simple directed graph with n vertices
Hamiltonian_path
Tsen's theorem (algebraic geometry) Weber's theorem (algebraic curves) Zariski's connectedness theorem (algebraic geometry) Zariski's main theorem (algebraic
List_of_theorems
Property of topological spaces
of a locally connected space. As an example, the notion of connectedness im kleinen at a point and its relation to local connectedness will be considered
Locally_connected_space
Continuous function on an interval takes on every value between its values at the ends
intermediate value theorem is closely linked to the topological notion of connectedness and follows from the basic properties of connected sets in metric
Intermediate_value_theorem
Space which has no holes through it
simply connected. The notion of simple connectedness is important in complex analysis because of the following facts: Cauchy's integral theorem states
Simply_connected_space
Theorem in topology
situation. Consequently, connectedness properties in R 2 {\displaystyle \mathbb {R} ^{2}} , such as the Jordan curve theorem, do not generalize to Z 2
Jordan_curve_theorem
Algebraic geometry theorem
used for induction steps.[example needed] Grothendieck's connectedness theorem "Bertini theorems", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Hartshorne
Theorem_of_Bertini
comparison theorem Grothendieck's connectedness theorem Grothendieck connection Grothendieck construction Grothendieck duality Grothendieck existence theorem Grothendieck
List of things named after Alexander Grothendieck
List_of_things_named_after_Alexander_Grothendieck
by Zariski's connectedness theorem, the last part in the above says that the fiber f ′ − 1 ( s ) {\displaystyle f'^{-1}(s)} is connected for any s ∈ S
Stein_factorization
Theorem in complex analysis
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard
Cauchy's_integral_theorem
Describes the fundamental group in terms of a cover by two open path-connected subspaces
Seifert–Van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), sometimes just called Van Kampen's theorem, expresses the
Seifert–Van_Kampen_theorem
Theorem in vector calculus
theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,
Stokes'_theorem
Concept in algebraic geometry
are connectedness theorems such as Grothendieck's connectedness theorem (a local analogue of the Bertini theorem) or the Fulton–Hansen connectedness theorem
Local_cohomology
Theorem on the equality of analytic functions
fact from which the theorem is established is the expandability of a holomorphic function into its Taylor series. The connectedness assumption on the domain
Identity_theorem
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces:
Uniformization_theorem
Need to sacrifice consistency or availability in the presence of network partitions
In database theory, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store can provide
CAP_theorem
Type of commutative ring in mathematics
Hartshorne's connectedness theorem: if R is a Cohen–Macaulay local ring of dimension at least 2, then Spec R minus its closed point is connected. The Segre
Cohen–Macaulay_ring
Concept in algebraic geometry
geometrically integral and all fibers are geometrically connected (by Zariski's connectedness theorem). In particular, for a fiber F = ∑ i = 1 n a i E i {\displaystyle
Canonical_bundle
Rigidity theorem in differential geometry
In the mathematical field of differential geometry, the fundamental theorem of surface theory deals with the problem of prescribing the geometric data
Bonnet_theorem
Concept of complex analysis
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions
Residue_theorem
Theorem in calculus relating line and double integrals
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R
Green's_theorem
Theorem about the range of an analytic function
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after
Picard_theorem
Equivalence of optimization problems
In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source
Max-flow_min-cut_theorem
Planar maps require at most four colors
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Relation between genus, degree, and dimension of function spaces over surfaces
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension
Riemann–Roch_theorem
In mathematics, the Cartan–Ambrose–Hicks theorem is a theorem of Riemannian geometry, according to which the Riemannian metric is locally determined by
Cartan–Ambrose–Hicks_theorem
Book by Marvin Minsky and Seymour Papert
such as the XOR function, and also the important connectedness predicate. The problem of connectedness is illustrated at the awkwardly colored cover of
Perceptrons_(book)
Theorem in electrical circuit analysis
stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources
Thévenin's_theorem
Singularities of holomorphic functions extend infinitely outward
existence part of Hartog's theorem is proved. Uniqueness is automatic from unique continuation, based on connectedness of G. The theorem does not hold when n
Hartogs's_extension_theorem
American mathematician (born 1939)
Springer-Verlag. ISBN 978-0-387-97495-8. MR 1153249. Fulton–Hansen connectedness theorem William Fulton at the Mathematics Genealogy Project Announcement
William Fulton (mathematician)
William_Fulton_(mathematician)
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Branch of mathematics
compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles
Topology
Well-quasi-ordering of finite trees
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under
Kruskal's_tree_theorem
low-dimensional hole. The concept of n-connectedness generalizes the concepts of path-connectedness and simple connectedness. An equivalent definition of homotopical
Homotopical_connectivity
On tangency patterns of circles
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible patterns of tangent circles among non-overlapping
Circle_packing_theorem
Statement in mathematical combinatorics
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)
Ramsey's_theorem
Graph that can be embedded in the plane
drawings on the sphere, usually with additional assumptions such as connectedness, is called a planar map. Although a plane graph has an external or unbounded
Planar_graph
{O}}_{Y}} or, equivalently, the geometric fibers are all connected (Zariski's connectedness theorem). It is also commonly called an algebraic fiber space
Contraction_morphism
Graph-theoretic description of polyhedra
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices
Steinitz's_theorem
Theorem in geometric topology
Poincaré is using the terminology of simple-connectedness in an unusual way, this says that a closed connected oriented manifold with the homology of a sphere
Poincaré_conjecture
Theorem in graph theory
In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number
Menger's_theorem
On the structure of complete Riemannian manifolds of non-positive sectional curvature
In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive
Cartan–Hadamard_theorem
Topics referred to by the same term
Dirac's theorem may refer to: Dirac's theorem on Hamiltonian cycles, the statement that an n-vertex graph in which each vertex has degree at least n/2
Dirac's_theorem
On graph coloring and neighborhood size
Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected graph in
Brooks'_theorem
Geometric theorem involving midpoints on a triangle
The midpoint theorem, midsegment theorem, or midline theorem states that if the midpoints of two sides of a triangle are connected, then the resulting
Midpoint_theorem_(triangle)
Theorem in differential geometry
In differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying
Gauss–Bonnet_theorem
Property of artificial neural networks
In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate
Universal approximation theorem
Universal_approximation_theorem
Group that is also a differentiable manifold with group operations that are smooth
important because of the following result that has simple connectedness as a hypothesis: Theorem: Suppose G {\displaystyle G} and H {\displaystyle H} are
Lie_group
On chains and antichains in partial orders
mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an
Dilworth's_theorem
Process of creating equivalent circuits
voltage sources connected in series, may be split into two grounded elements with corresponding impedances. There is also a dual Miller theorem with regards
Miller_theorem
Theorem concerning ratios of line segments
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry
Intercept_theorem
Gives a homomorphism from homotopy groups to homology groups
In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz
Hurewicz_theorem
Mathematical concept for comparing objects
Then the following three connected theorems hold: ~ partitions A into equivalence classes. (This is the Fundamental Theorem of Equivalence Relations,
Equivalence_relation
Topics referred to by the same term
In mathematics, Chow's theorem may refer to a number of theorems due to Wei-Liang Chow: Chow's theorem: Any analytic subvariety in projective space is
Chow's_theorem
Algebraic variety
rationally connected if every two points are connected by a rational curve contained in the variety. This definition differs from that of path connectedness only
Rational_variety
Statement about integration on manifolds
generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about
Generalized_Stokes_theorem
Key results in general relativity on gravitational singularities
when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Topics referred to by the same term
4-vertex-connected planar graphs Tutte's theorem on perfect matchings, a characterization of the graphs having perfect matchings Tutte's spring theorem, on
Tutte's_theorem
Mathematical theorem
complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number plane
Riemann_mapping_theorem
On Hamiltonian cycles in planar graphs
theory, a theorem of W. T. Tutte states that every 4-vertex-connected planar graph has a Hamiltonian cycle. It strengthens an earlier theorem of Hassler
Tutte's theorem on Hamiltonian cycles
Tutte's_theorem_on_Hamiltonian_cycles
Theorem in differential topology
topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real m-dimensional
Whitney_embedding_theorem
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
Theorem in projective geometry
In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem, Latin for mystical hexagram) states that if six arbitrary points
Pascal's_theorem
Theorem in physics
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with
Bell's_theorem
Theorem on Hamiltonian graphs
Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that, if G {\displaystyle G} is a 2-vertex-connected graph
Fleischner's_theorem
On the number of spanning trees in a graph
mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph.
Kirchhoff's_theorem
Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices
Ptolemy's_theorem
Area of discrete mathematics
requirements of Steinitz's theorem, stating that every convex polyhedron is 3-vertex connected planar graph. The planar graph remains connected whenever any two
Graph_theory
Theorem in topology
In mathematics, Janiszewski's theorem, named after the Polish mathematician Zygmunt Janiszewski, is a result concerning the topology of the plane or extended
Janiszewski's_theorem
Theorem on the behavior of dynamical systems
In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder
Poincaré–Bendixson_theorem
Number divisible only by 1 and itself
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself
Prime_number
On horizontal paths in a sub-Riemannian manifold
sub-Riemannian geometry, the Chow–Rashevskii theorem (also known as Chow's theorem) asserts that any two points of a connected sub-Riemannian manifold, endowed with
Chow–Rashevskii_theorem
On forbidden subgraphs in planar graphs
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states
Kuratowski's_theorem
Integral criterion for holomorphy
mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic. Morera's theorem states that a continuous
Morera's_theorem
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
On representability of a contravariant functor on the category of connected CW complexes
theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected
Brown's representability theorem
Brown's_representability_theorem
Concept in topology
h-cobordism theorem showed that (simply connected) manifolds of dimension at least 5 are much easier than those of dimension 3 or 4. The proof of the theorem depends
H-cobordism
Bound on eigenvalues
In mathematics, the Gershgorin circle theorem (also called sometimes Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix. It
Gershgorin_circle_theorem
On structure of ω-bounded connected surfaces
In mathematics, the bagpipe theorem of Peter Nyikos describes the structure of the connected (but possibly non-paracompact) ω-bounded surfaces by showing
Bagpipe_theorem
Complete manifolds of non-negative sectional curvature largely reduce to the compact case
In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature
Soul_theorem
DC circuit analysis technique
In direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of
Norton's_theorem
Equivalent properties in a normal connected locally connected topological space
Phragmén–Brouwer theorem, introduced by Lars Edvard Phragmén and Luitzen Egbertus Jan Brouwer, states that if X is a normal connected locally connected topological
Phragmen–Brouwer_theorem
Geodesic maps preserve the property of having constant curvature
−1/ngil(∂i ρl − ρi ρl). By connectedness of the manifold, this local constancy implies global constancy. Beltrami's theorem may be phrased in the language
Beltrami's_theorem
au théorème de connexité (Zariski holomorphic functions, Zariski connectedness theorem) Jean Dieudonné, Extensions de représentations linéaires de groupes
Séminaire Nicolas Bourbaki (1950–1959)
Séminaire_Nicolas_Bourbaki_(1950–1959)
Planar maps require at most five colors
The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world
Five_color_theorem
Evaluates a line integral through a gradient field using the original scalar field
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated
Gradient_theorem
Square matrices satisfy their characteristic equation
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix
Cayley–Hamilton_theorem
Partition of a graph whose components are reachable from all vertices
Robbins' theorem, an undirected graph may be oriented in such a way that it becomes strongly connected, if and only if it is 2-edge-connected. One way
Strongly_connected_component
Theorem on edge-disjoint spanning trees
In graph theory, the Nash-Williams theorem is a tree-packing theorem that describes how many edge-disjoint spanning trees (and more generally forests)
Nash-Williams_theorem
Property of a relation on a set
so that x R y {\displaystyle x\mathrel {R} y} (see serial relation). Connectedness features prominently in the definition of total orders: a total (or
Connected_relation
Property of a space in which the local dimensionality is the same everywhere
from the original on 29 June 2020. Sawant, Anand P. Hartshorne's Connectedness Theorem (PDF). p. 3. Archived from the original (PDF) on 24 June 2015. Bender
Equidimensionality
CONNECTEDNESS THEOREM
CONNECTEDNESS THEOREM
CONNECTEDNESS THEOREM
CONNECTEDNESS THEOREM
Girl/Female
Greek American Welsh Latin
Holy one.
Male
Greek
(ἈÏιδαίος) Greek name of Persian origin, ARIDAIOS means "strong."Â
Girl/Female
Haryanvi, Indian, Kannada, Telugu
Fearless; Surprise; Very Nice
Boy/Male
Hindu, Indian
Invisible
Girl/Female
Hindu, Indian
Goddess Sita
Boy/Male
Arabic
Love; Wish; Desire
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Chipping of Birds
Girl/Female
Biblical
Desirable.
Surname or Lastname
English
English : habitational name from Gaddesden in Hertfordshire, recorded in Domesday Book as Gatesdene, from an Old English personal name Gǣte(n) + Old English denu ‘valley’.
Boy/Male
Arabic, Muslim
Goodness; Health; Safe
CONNECTEDNESS THEOREM
CONNECTEDNESS THEOREM
CONNECTEDNESS THEOREM
CONNECTEDNESS THEOREM
CONNECTEDNESS THEOREM
n.
A collected state of the mind; self-possession.
n.
The state of being conceited; conceit; vanity.
n.
A theorem or proposition so easy of demonstration as to be almost self-evident.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
The quality of being desultory or without order or method; unconnectedness.
a.
Theorematic.
n.
Conceitedness.
v. t.
To formulate into a theorem.
n.
Obstinacy in holding to one's belief or impression; opiniativeness; conceitedness.
a.
Alt. of Theorematical
n.
A numerical coefficient in any particular case of the binomial theorem.
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
n.
A statement of a principle to be demonstrated.
n.
One who constructs theorems.
n.
That which is considered and established as a principle; hence, sometimes, a rule.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.