Compactness (mathematics) | Properties of topological spaces

Metacompact space

In the 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 any open cover of the topological space, there is a refinement that is again an open cover with the property that every point is contained only in finitely many sets of the refining cover. A space is countably metacompact if every countable open cover has a point-finite open refinement. (Wikipedia).

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Related pages

Compact space | Topological space | Metric space | Shrinking space | Realcompact space | Tube lemma | Countable set | General topology | Tychonoff space | Mathematics | Glossary of topology | Normal space | Refinement (topology) | Mesocompact space | Pseudocompact space | Paracompact space | Moore plane | Dieudonné plank