compact subset

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• 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

• Compact-open topology — In mathematics, the compact open topology is a topology defined on the set of continuous maps between two topological spaces. The compact open topology is one of the commonly used topologies on function spaces, and is applied in homotopy theory… …   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

• Compact (disambiguation) — Compact may mean: * Compact (newspaper), a broadsheet quality newspaper printed in a tabloid format. * Compact (soap opera), a 1960s British soap opera. * a diplomatic contract or covenant among parties, sometimes known as a pact, treaty, or an… …   Wikipedia

• Compact element — In the mathematical area of order theory, the compact or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non empty directed set that does not already contain members above the compact… …   Wikipedia

• Compact convergence — In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence which generalizes the idea of uniform convergence. It is associated with the compact open topology. Contents 1 Definition 2 Examples 3 Properties …   Wikipedia

• compact — I. adjective Etymology: Middle English, firmly put together, from Latin compactus, from past participle of compingere to put together, from com + pangere to fasten more at pact Date: 14th century 1. predominantly formed or filled ; composed, made …   New Collegiate Dictionary

• Compact complement topology — In mathematics, the compact complement topology is a topology defined on the set of real numbers, defined by declaring a subset open if and only if it is either empty or its complement is compact in the standard Euclidean topology on …   Wikipedia

• compact space — noun Any topological subset of Euclidean space that is a compact set …   Wiktionary

• Locally compact space — In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.Formal definitionLet X be a topological space. The… …   Wikipedia