Definition of Metacompact. Meaning of Metacompact. Synonyms of Metacompact

Here you will find one or more explanations in English for the word Metacompact. Also in the bottom left of the page several parts of wikipedia pages related to the word Metacompact and, of course, Metacompact synonyms and on the right images related to the word Metacompact.

Definition of Metacompact

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Meaning of Metacompact from wikipedia

- mathematical field of general topology, a topological space is said to be metacompact if every open cover has a point-finite open refinement. That is, given...
- a compact space is paracompact. The product of a metacompact space and a compact space is metacompact. Both these results can be proved by the tube lemma...
- only finitely many members of U . {\displaystyle {\mathcal {U}}.} A metacompact space is a topological space in which every open cover admits a point-finite...
- and pseudocompact, but neither weakly countably compact nor countably metacompact, hence not compact. Cofinite topology List of topologies Steen, Lynn...
- (or equivalently that every open cover has a countable refinement); Metacompact if every open cover has a point-finite open refinement; Paracompact if...
- definitions of paracompact space and metacompact space, and this is the reason why every paracompact space is metacompact. If a collection of sets is locally...
- neither compact, sequentially compact, countably compact, paracompact nor metacompact (although it is orthocompact). However, since X is hyperconnected, it...
- Carathéodory's extension theorem Geometric set cover problem Dimension theory Metacompact space Point-finite collection Lebesgue, Henri (1921). "Sur les correspondances...
- open cover is interior preserving. Hence, we have the following: every metacompact space, and in particular, every paracompact space, is orthocompact. Useful...
- theorem Eberlein compactum Exhaustion by compact sets Lindelöf space Metacompact space Noetherian topological space Orthocompact space Paracompact space...