closure operator

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• 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 (mathematics) — For other uses, see Closure (disambiguation). In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers… …   Wikipedia

• Closure (topology) — For other uses, see Closure (disambiguation). In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are near S. A point which is in the… …   Wikipedia

• Closure — may refer to: Closure (container) used to seal a bottle, jug, jar, can, or other container Closure (wine bottle), a stopper Closure (business), the process by which an organization ceases operations Closure (philosophy), a principle in… …   Wikipedia

• Closure (computer science) — In computer science, a closure (also lexical closure, function closure, function value or functional value) is a function together with a referencing environment for the non local variables of that function.[1] A closure allows a function to… …   Wikipedia

• Operator topology — In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(H) of bounded linear operators on a Hilbert space H. Contents 1 Introduction 2 List of topologies on B(H) 3 …   Wikipedia

• Operator algebra — In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings. Although it is usually classified as a branch of functional… …   Wikipedia

• Preclosure operator — In topology, a preclosure operator, or Čech closure operator is a map between subsets of a set, similar to a topological closure operator, except that it is not required to be idempotent. That is, a preclosure operator obeys only three of the… …   Wikipedia

• Kuratowski closure axioms — In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms which can be used to define a topological structure on a set. They are equivalent to the more commonly used open set definition. They were first… …   Wikipedia

• Closed operator — In mathematics, specifically in functional analysis, closed linear operators are an important class of linear operators on Banach spaces. They are more general than bounded operators, and therefore not necessarily continuous, but they still… …   Wikipedia

• Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia