locally compact

locally compact
(of a topological space) That for every point of the given topological space, there is a neighborhood of that point whose closure is compact.

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  • 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

  • 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

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  • locally compact space — Math. a topological space in which each point has a neighborhood that is compact. * * * …   Universalium

  • locally compact space — Math. a topological space in which each point has a neighborhood that is compact …   Useful english dictionary

  • Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   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

  • Locally connected space — In this topological space, V is a neighbourhood of p and it contains a connected neighbourhood (the dark green disk) that contains p. In topology and other branches of mathematics, a topological space X is locally connected if every point admits… …   Wikipedia

  • Locally regular space — In mathematics, particularly topology, a topological space X is locally regular if intuitively it looks locally like a regular space. More precisely, a locally regular space satisfies the property that each point of the space belongs to a subset… …   Wikipedia

  • Locally normal space — In mathematics, particularly topology, a topological space X is locally normal if intuitively it looks locally like a normal space. More precisely, a locally normal space satisfies the property that each point of the space belongs to a… …   Wikipedia

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