Lindelöf space


Lindelöf space
A topological space such that any open cover of the space has a countable subcover.

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  • Lindelöf space — In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. A Lindelöf space is a weakening of the more commonly used notion of compactness , which requires the existence of a finite subcover.A… …   Wikipedia

  • Lindelöf space — /lin deuh lof , lawf , luef /, Math. a topological space having the property that every cover consisting of open sets has a subcover consisting of a countable number of subsets. [after Ernst Lindelöf (1870 1946), Finnish topologist] * * * …   Universalium

  • Lindelöf space — /lin deuh lof , lawf , luef /, Math. a topological space having the property that every cover consisting of open sets has a subcover consisting of a countable number of subsets. [after Ernst Lindelöf (1870 1946), Finnish topologist] …   Useful english dictionary

  • space — 1. noun /speɪs/ a) The intervening contents of a volume. If it be only a Single Letter or two that drops, he thruſts the end of his Bodkin between every Letter of that Word, till he comes to a Space: and then perhaps by forcing thoſe Letters… …   Wiktionary

  • Lindelöf's lemma — In mathematics, Lindelöf s lemma is a simple but useful lemma in topology on the real line, named for the Finnish mathematician Ernst Leonard Lindelöf.tatement of the lemmaLet the real line have its usual Borel topology. Then every open subset of …   Wikipedia

  • Ernst Leonard Lindelöf — Ernst Leonard Lindelöf, (7 March 1870 ndash;4 June 1946) was a Finnish topologist after whom Lindelöf space is named; he was the son of Leonard Lorenz Lindelöf and brother of the philologist Uno Lorenz Lindelöf.Lindelöf studied at the University… …   Wikipedia

  • Σ-compact space — In mathematics, a topological space is said to be sigma; compact if it is the union of countably many compact subspaces. A space is said to be sigma; locally compact if it is both sigma; compact and locally compact.Properties and Examples* Every… …   Wikipedia

  • Ernst Leonard Lindelöf —  Ne doit pas être confondu avec le producteur américain de télévision Damon Lindelof. Ernst Leonard Lindelöf (7 mars 1870 – 4 juin 1946), est un mathématicien finlandais qui travailla principalement en analyse complexe et en théorie des… …   Wikipédia en Français

  • 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

  • Paracompact space — In mathematics, a paracompact space is a topological space in which every open cover admits a locally finite open refinement. Paracompact spaces are sometimes also required to be Hausdorff. Paracompact spaces were introduced by Dieudonné (1944).… …   Wikipedia