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compact closure

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  • 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

  • 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

  • Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …   Wikipedia

  • Compact operator — In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y. Such an… …   Wikipedia

  • Continuous functions on a compact Hausdorff space — In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by C(X), is a vector… …   Wikipedia

  • Locally compact group — In mathematics, a locally compact group is a topological group G which is locally compact as a topological space. Locally compact groups are important because they have a natural measure called the Haar measure. This allows one to define… …   Wikipedia

  • Spectral theory of compact operators — In functional analysis, compact operators are linear operators that map bounded sets to precompact ones. Compact operators acting on a Hilbert space H is the closure of finite rank operators in the uniform operator topology. In general, operators …   Wikipedia

  • Relatively compact subspace — In mathematics, a relatively compact subspace (or relatively compact subset) Y of a topological space X is a subset whose closure is compact.Since closed subsets of compact spaces are compact, every set in a compact space is relatively compact.… …   Wikipedia

  • locally compact — adjective (of a topological space) That for every point of the given topological space, there is a neighborhood of that point whose closure is compact …   Wiktionary

  • Corona set — In mathematics, the corona or corona set of a topological space X is the complement βXX of the space in its Stone–Čech compactification βX. A topological space is said to be σ compact if it is the union of countably many compact subspaces, and… …   Wikipedia

  • Traced monoidal category — In category theory, a traced monoidal category is a category with some extra structure which gives a reasonable notion of feedback.A traced symmetric monoidal category is a symmetric monoidal category C together with a family of… …   Wikipedia

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