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In projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and
Intersection_theorem
On decreasing nested sequences of non-empty compact sets
Cantor's intersection theorem, also called Cantor's nested intervals theorem, refers to two closely related theorems in general topology and real analysis
Cantor's_intersection_theorem
Theorem about the intersections of d-dimensional convex sets
Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published
Helly's_theorem
Theorem in topology
intersection theorem is a result in general topology that gives a sufficient condition for a nested sequence of sets to have a non-empty intersection
Kuratowski's intersection theorem
Kuratowski's_intersection_theorem
Theorem in plane geometry
two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by
Monge's_theorem
M finitely-generated. One consequence of the lemma is the Krull intersection theorem. The result is also used to prove the exactness property of completion
Artin–Rees_lemma
Concerns 3 circles through triples of points on the vertices and sides of a triangle
Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a
Miquel's_theorem
Theorem in projective geometry
Desargues's theorem states that the truth of the first condition is necessary and sufficient for the truth of the second. This intersection theorem is true
Desargues's_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
Number of intersection points of algebraic curves and hypersurfaces
number of intersection points given by the product of their degrees. However, Newton had stated the theorem as early as 1665. The general theorem was later
Bézout's_theorem
Mathematical ring with well-behaved ideals
general theorems on rings rely heavily on the Noetherian property (for example, the Lasker–Noether theorem and the Krull intersection theorem). Noetherian
Noetherian_ring
Theorem in mathematical logic
compact space has a non-empty intersection if every finite subcollection has a non-empty intersection. The compactness theorem is one of the two key properties
Compactness_theorem
(Mathematical) ring with a unique maximal ideal
}m^{i}=\{0\}} (Krull's intersection theorem), and it follows that R with the m-adic topology is a Hausdorff space. The theorem is a consequence of the
Local_ring
On triangles inscribed in a circle with a diameter as an edge
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle
Thales's_theorem
On topological spaces where the intersection of countably many dense open sets is dense
The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient
Baire_category_theorem
Theorem in Euclidean geometry
theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. This theorem refers
Mohr–Mascheroni_theorem
Upper bound on intersecting set families
In mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common.
Erdős–Ko–Rado_theorem
Geometry theorem relating the line segments created by intersecting chords in a circle
quadrilateral. The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called
Intersecting_chords_theorem
Group of mathematical theorems
specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients
Isomorphism_theorems
Theorem in extremal set theory
In extremal set theory, the Ahlswede–Khachatrian theorem generalizes the Erdős–Ko–Rado theorem to t-intersecting families. Given parameters n, k and t
Ahlswede–Khachatrian_theorem
Subset of Euclidean space is compact if and only if it is closed and bounded
In real analysis in mathematics, the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S {\displaystyle S} of Euclidean
Heine–Borel_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Topics referred to by the same term
B Cantor's isomorphism theorem: every two countable dense unbounded linear orders are isomorphic Cantor's intersection theorem: a decreasing nested sequence
Cantor's theorem (disambiguation)
Cantor's_theorem_(disambiguation)
Polish mathematician and logician
name include Kuratowski's theorem, Kuratowski closure axioms, Kuratowski-Zorn lemma and Kuratowski's intersection theorem. Kazimierz Kuratowski was born
Kazimierz_Kuratowski
Geometry theorem
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that if A , B , C {\displaystyle A,B,C} is one set of collinear points
Pappus's_hexagon_theorem
Theorem on cyclic quadrilateral
In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular
Brahmagupta_theorem
Set of elements common to all of some sets
In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing
Intersection_(set_theory)
Branch of algebraic geometry
For example, a theorem of Michael Freedman states that simply connected compact 4-manifolds are (almost) determined by their intersection forms up to homeomorphism
Intersection_theory
On when a definite intersection form of a smooth 4-manifold is diagonalizable
Donaldson's theorem states that a definite intersection form of a closed, oriented, smooth manifold of dimension 4 is diagonalizable. If the intersection form
Donaldson's_theorem
Shared independent set of two matroids
graphs and finding arborescences in directed graphs. The matroid intersection theorem, due to Jack Edmonds, says that for any two matroids M 1 = ( E ,
Matroid_intersection
Theorem in topology
{\displaystyle C} has no self-intersection points. With these definitions, the Jordan curve theorem can be stated as follows: Theorem—Let C {\displaystyle C}
Jordan_curve_theorem
Describes the fundamental group in terms of a cover by two open path-connected subspaces
with say 402 path components and whose intersection has say 1004 path components. The interpretation of this theorem as a calculational tool for "fundamental
Seifert–Van_Kampen_theorem
On the intersection form of a smooth, closed 4-manifold with a spin structure
of its intersection form, a quadratic form on the second cohomology group H 2 ( M ) {\displaystyle H^{2}(M)} , is divisible by 16. The theorem is named
Rokhlin's_theorem
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
On tangency patterns of circles
packing in the plane whose intersection graph is isomorphic to G {\displaystyle G} . A stronger form of the circle packing theorem applies to any polyhedral
Circle_packing_theorem
Property in general topology
the finite intersection property has non-empty intersection. This formulation of compactness is used in some proofs of Tychonoff's theorem. Another common
Finite_intersection_property
Statement about cubic curves in the projective plane
Cayley–Bacharach theorem arises for high degree because the number of intersection points of two curves of degree d, namely d 2 (by Bézout's theorem), grows faster
Cayley–Bacharach_theorem
Algebraic variety of dimension two
restriction (self-intersection number must be −1). One of the fundamental theorems for the birational geometry of surfaces is Castelnuovo's theorem. This states
Algebraic_surface
algebraic geometry, the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber or BBDG decomposition theorem is a set of results concerning the
Decomposition theorem of Beilinson, Bernstein and Deligne
Decomposition_theorem_of_Beilinson,_Bernstein_and_Deligne
Theorem relating the diameter of a point set to the minimum radius of an enclosing ball
d/2} ball centered at a point of this intersection contains all of S {\displaystyle S} . Versions of Jung's theorem for various non-Euclidean geometries
Jung's_theorem
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result
Bolzano–Weierstrass_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
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
American/Canadian mathematician and computer scientist
the matroid intersection theorem, a very general combinatorial min-max theorem which, in modern terms, showed that the matroid intersection problem lay
Jack_Edmonds
On when a space equals the closed convex hull of its extreme points
and convex analysis Helly's theorem – Theorem about the intersections of d-dimensional convex sets Radon's theorem – Theorem in geometry about convex sets
Krein–Milman_theorem
Area of discrete mathematics
Koebe–Andreev–Thurston theorem, the intersection graphs of non-crossing circles are exactly the planar graphs. Scheinerman's theorem states that every planar
Graph_theory
Concept in commutative algebra
that case, the 𝔞-adic topology is called separated. By Krull's intersection theorem, if R is a Noetherian ring which is an integral domain or a local
I-adic_topology
Equivalence of distributive lattices and set families
similarly named results, see Birkhoff's theorem (disambiguation). In mathematics, Birkhoff's representation theorem for distributive lattices states that
Birkhoff's representation theorem
Birkhoff's_representation_theorem
topology, a saturated set is a subset of a topological space equal to an intersection of (an arbitrary number of) open sets. Let S {\displaystyle S} be a subset
Saturated set (intersection of open sets)
Saturated_set_(intersection_of_open_sets)
In mathematics, a statement that has been proven
mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
resolution, then R {\displaystyle R} is a Cohen–Macaulay ring. The Intersection Theorem. If M ⊗ R N ≠ 0 {\displaystyle M\otimes _{R}N\neq 0} has finite length
Homological conjectures in commutative algebra
Homological_conjectures_in_commutative_algebra
Technique invented by Paul Cohen for proving consistency and independence results
that any filter is closed under finite intersection. Therefore, by Cantor's intersection theorem, the intersection of all the elements in any filter is
Forcing_(mathematics)
Polynomial ideals are finitely generated
commutative algebra. In particular, the basis theorem implies that every algebraic set is the intersection of a finite number of hypersurfaces. Another
Hilbert's_basis_theorem
3 intersections of any triangle's adjacent angle trisectors form an equilateral triangle
In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral
Morley's_trisector_theorem
Quadrilateral whose vertices lie on a circle
Brahmagupta's theorem states that for a cyclic quadrilateral that is also orthodiagonal, the perpendicular from any side through the point of intersection of the
Cyclic_quadrilateral
Theorem about triangles
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle △ABC, let the lines AO, BO, CO be drawn from the vertices to a common
Ceva's_theorem
Mathematical proposition equivalent to the axiom of choice
the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space
Zorn's_lemma
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 algebra that studies commutative rings
is the case, in particular of Lasker–Noether theorem, the Krull intersection theorem, and Nakayama's lemma. Furthermore, if a ring is Noetherian, then
Commutative_algebra
German mathematician (1899–1971)
topology Krull–Azumaya theorem Krull–Schmidt category Krull–Schmidt theorem Krull's intersection theorem Krull's principal ideal theorem Krull's separation
Wolfgang_Krull
Theorem about zeros of holomorphic functions
multiplicity. This theorem assumes that the contour ∂ K {\displaystyle \partial K} is simple, that is, without self-intersections. Rouché's theorem is an easy
Rouché's_theorem
Mathematical theorem
In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was
Riemann–Roch theorem for surfaces
Riemann–Roch_theorem_for_surfaces
In algebra, expression of an ideal as the intersection of ideals of a specific type
Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary
Primary_decomposition
Theorem in functional analysis
and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of
Banach–Alaoglu_theorem
Equivalence class of objects sharing local properties at a point in a topological space
derivatives vanish. If this ring were Noetherian, then the Krull intersection theorem would imply that a smooth function whose Taylor series vanished would
Germ_(mathematics)
1995 publication in mathematics
Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Product of any collection of compact topological spaces is compact
Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named
Tychonoff's_theorem
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
Ranges of numbers contained in each other
behaviour of certain differential equations. Bisection Cantor's intersection theorem Königsberger, Konrad (2004). Analysis 1. Springer. p. 11. ISBN 354040371X
Nested_intervals
Mathematical construction
smooth functions at the origin is a non-Noetherian ring. The Krull intersection theorem says that this cannot happen for a Noetherian ring.) On an affine
Stalk_(sheaf)
Universality of construction using just a straightedge and a single circle with center
In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states
Poncelet–Steiner_theorem
Connects homology and cohomology groups for oriented closed manifolds
1895 paper Analysis Situs, Poincaré tried to prove the theorem using topological intersection theory, which he had invented. Criticism of his work by
Poincaré_duality
Type of commutative ring in mathematics
who proved the unmixedness theorem for polynomial rings, and for Irvin Cohen (1946), who proved the unmixedness theorem for formal power series rings
Cohen–Macaulay_ring
Theorems that help decompose a finite group based on prime factors of its order
specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow
Sylow_theorems
Mathematical theory
results such as a Riemann-Roch theorem, a Noether formula, a Hodge index theorem and the nonnegativity of the self-intersection of the dualizing sheaf in this
Arakelov_theory
Derives a pentagram from five chained circles centered on a common sixth circle
second intersection points forms a pentagram whose points lie on the circles themselves. Clifford's circle theorems Miquel's theorem Six circles theorem Seven
Five_circles_theorem
Mathematical problem
Problem G10, ISBN 978-0-387-97506-1 Frankl, P.; Wilson, R.M. (1981), "Intersection theorems with geometric consequences", Combinatorica, 1 (4): 357–368, doi:10
Hadwiger–Nelson_problem
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
Theorem in geometry about convex sets
have a nonempty intersection. This same general statement, when applied to a hypersphere instead of a simplex, gives the Borsuk–Ulam theorem, that ƒ must
Radon's_theorem
Theorem in differential topology
^{2m}} with transverse self-intersections. These are known to exist from Whitney's earlier work on the weak immersion theorem. Transversality of the double
Whitney_embedding_theorem
In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V
Hodge_index_theorem
Fundamental theorem in mathematical logic
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability
Gödel's_completeness_theorem
Gives a lower bound on the number of lines determined by n points in a projective plane
In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős in 1948, states a lower bound on
De Bruijn–Erdős theorem (incidence geometry)
De_Bruijn–Erdős_theorem_(incidence_geometry)
Theorem extending pre-measures to measures
In measure theory, Carathéodory's extension theorem (named after the mathematician Constantin Carathéodory) states that any pre-measure defined on a given
Carathéodory's extension theorem
Carathéodory's_extension_theorem
In algebra, completion w.r.t. powers of an ideal
intersection reduces to the zero element of the ring; by the Krull intersection theorem, this is the case for any commutative Noetherian ring which is an
Completion_of_a_ring
Movement with a fixed point is rotation
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the body remains
Euler's_rotation_theorem
Angle formed in the interior of a circle
its intersection points equals half of the central angle subtended by the chord. See also Tangent lines to circles. The inscribed angle theorem is used
Inscribed_angle
Principle in compass and straightedge constructions
In geometry, the compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these
Compass_equivalence_theorem
Certain dynamical systems will eventually return to (or approximate) their initial state
In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, almost
Poincaré_recurrence_theorem
Algebraic geometry theorem
\mathbf {P} ^{n}} . The theorem of Bertini states that the set of hyperplanes not containing X and with smooth intersection with X contains an open dense
Theorem_of_Bertini
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
Theorem in geometry
In Euclidean geometry, Varignon's theorem holds that the midpoints of the sides of an arbitrary quadrilateral form a parallelogram, called the Varignon
Varignon's_theorem
Algebraic structure with addition and multiplication
if R is a Noetherian local ring with maximal ideal I, by Krull's intersection theorem. The construction is especially useful when I is a maximal ideal
Ring_(mathematics)
Collection of sets in which every two sets have the same intersection
where vertices represent the sets and edges are colored by intersection size, Ramsey's theorem guarantees the existence of a large monochromatic clique
Sunflower_(mathematics)
Fixed-point theorem for smooth manifolds
M\times M} , and the Lefschetz number thereby becomes an intersection number. The Atiyah–Bott theorem is an equation in which the LHS must be the outcome of
Atiyah–Bott fixed-point theorem
Atiyah–Bott_fixed-point_theorem
Cantor's intersection theorem Cantor's isomorphism theorem Cantor's first set theory article Cantor's leaky tent Cantor's paradox Cantor's theorem Cantor–Bendixson
List of things named after Georg Cantor
List_of_things_named_after_Georg_Cantor
Concept in commutative algebra
that is, can be written as an intersection of finitely many primary ideals. This result is known as the Lasker–Noether theorem. Consequently, an irreducible
Primary_ideal
Graph representing intersections between given sets
the intersection graph of unit disks in the plane. A circle graph is the intersection graph of a set of chords of a circle. The circle packing theorem states
Intersection_graph
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
INTERSECTION THEOREM
INTERSECTION THEOREM
INTERSECTION THEOREM
INTERSECTION THEOREM
Boy/Male
Tamil
Pranjal | பà¯à®°à®¾à®‚ஜலÂ
Honest, Self-respecting, Sincere, Simple
Boy/Male
Hindu, Indian, Latin
Rising Star
Boy/Male
Tamil
Reliable, Trustworthy, Faithful
Boy/Male
British, English
Spear; Wedge-shaped Object; Triangular Shaped Piece of Land
Boy/Male
Biblical
Ethiopians, blackness.
Boy/Male
Sikh
In Love with God
Boy/Male
Hindu
Dronacharya & Shiva
Surname or Lastname
Altered spelling of German Luhmann or Lohmann.English
Altered spelling of German Luhmann or Lohmann.English : unexplained.
Boy/Male
Arabic, Indian, Muslim
Rightly Guided
Boy/Male
French
Named for Saint Denys.
INTERSECTION THEOREM
INTERSECTION THEOREM
INTERSECTION THEOREM
INTERSECTION THEOREM
INTERSECTION THEOREM
v. t.
Intersection, as of two paths or roads.
n.
The act of interjecting or throwing between; also, that which is interjected.
n.
A line of division or intersection; as, the tendinous inscriptions, or intersections, of a muscle.
n.
The point or line in which one line or surface cuts another.
n.
The act of intervening; interposition.
n.
An intervening period of time; interval.
n.
Intervention; interposition.
n.
The act by which a third person, to protect his own interest, interposes and becomes a party to a suit pending between other parties.
n.
Any interference that may affect the interests of others; especially, of one or more states with the affairs of another; mediation.
a.
Pertaining to, or formed by, intersections.
n.
The act of intercepting; as, interception of a letter; interception of the enemy.
n.
A word or form of speech thrown in to express emotion or feeling, as O! Alas! Ha ha! Begone! etc. Compare Exclamation.
n.
Intimate connection.
n.
Interposition; intervention.
n.
The act, state, or place of intersecting.
n.
Intervention; interposition.
a.
Intersecting at acute angles.
n.
Clay intersecting a vein.
n.
Mutual or reciprocal action or influence; as, the interaction of the heart and lungs on each other.
n.
Interception; a stopping / obstruction.