closure theorem

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• Closure with a twist — is a property of subsets of an algebraic structure. A subset Y of an algebraic structure X is said to exhibit closure with a twist if for every two elements there exists an automorphism ϕ of X and an element such that …   Wikipedia

• Closure operator — In mathematics, a closure operator on a set S is a function cl: P(S) → P(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S. X ⊆ cl(X) (cl is extensive) X ⊆ Y implies cl(X) ⊆ cl(Y)   (cl… …   Wikipedia

• Closure problem — A Closure problem is a problem in graph theory for finding a set of vertices in a directed graph such that there are no edges from the set to the rest of the graph. More specifically, the minimum closure problem asks for a set of this type with… …   Wikipedia

• Fixed point theorem — In mathematics, a fixed point theorem is a result saying that a function F will have at least one fixed point (a point x for which F ( x ) = x ), under some conditions on F that can be stated in general terms. Results of this kind are amongst the …   Wikipedia

• Open mapping theorem (functional analysis) — In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is… …   Wikipedia

• Ore's theorem — For Ore s theorem in ring theory, see Ore condition. Ore s theorem is a result in graph theory proved in 1960 by Norwegian mathematician Øystein Ore. It gives a sufficient condition for a graph to be Hamiltonian, essentially stating that a graph… …   Wikipedia

• Fundamental theorem of algebra — In mathematics, the fundamental theorem of algebra states that every non constant single variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed.Sometimes,… …   Wikipedia

• Von Neumann bicommutant theorem — In mathematics, the von Neumann bicommutant theorem in functional analysis relates the closure of a set of bounded operators on a Hilbert space in certain topologies to the bicommutant of that set. In essence, it is a connection between the… …   Wikipedia

• Kronecker's theorem — In mathematics, Kronecker s theorem, named after Leopold Kronecker, is a result in diophantine approximations applying to several real numbers xi , for 1 ≤ i ≤ N , that generalises dubious the equidistribution theorem, which implies that an… …   Wikipedia

• Continuous mapping theorem — In probability theory, the continuous mapping theorem states that continuous functions are limit preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps… …   Wikipedia

• Krein–Milman theorem — In mathematics, more precisely in functional analysis, the Krein–Milman theorem is a statement about convex sets. A particular case of this theorem, which can be easily visualized, states that given a convex polygon, one only needs the corners of …   Wikipedia