- paracompact
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In which every open cover admits an open locally finite refinement.
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paracompact
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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
Espace Paracompact — Un espace topologique est dit paracompact si tout recouvrement ouvert admet un raffinement (ouvert) localement fini. Cette définition a été introduite par le mathématicien français Dieudonné. On rappelle qu un recouvrement (Xi) d un espace… … Wikipédia en Français
Espace paracompact — Un espace topologique est dit paracompact s il est séparé, et si tout recouvrement ouvert admet un raffinement (ouvert) localement fini[1]. Cette définition a été introduite par le mathématicien français Jean Dieudonné. On rappelle qu un… … Wikipédia en Français
A-paracompact space — In mathematics, in the field of topology, a topological space is said to be a paracompact if every open cover of the topological space has a locally finite refinement. Unlike in the definition of paracompactness we do not insist that the… … Wikipedia
Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… … Wikipedia
Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… … Wikipedia
Topological property — In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms. That is, a property of spaces is a topological property if whenever a space … Wikipedia
Metrization theorem — In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space (X,τ) is said to be metrizable if there is a metric such that the topology induced by d… … Wikipedia
Normal space — Separation Axioms in Topological Spaces Kolmogorov (T0) version T0 | T1 | T2 | T2½ | completely T2 T3 | T3½ | T4 | T5 | T6 In topology and related branches of mathematics, a no … Wikipedia
Injective sheaf — In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext .). There is a further group of related concepts applied to sheaves: flabby … Wikipedia
