metacompact space
1Metacompact space — In mathematics, in the 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 which is again… …
2space — 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… …
3Paracompact 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).… …
4Shrinking space — In mathematics, in the field of topology, a topological space is said to be a shrinking space if every open cover admits a shrinking. A shrinking of an open cover is another open cover indexed by the same indexing set, with the property that the… …
5Orthocompact space — In mathematics, in the field of general topology, a topological space is said to be orthocompact if every open cover has an interior preserving open refinement. That is, given an open cover of the topological space, there is a refinement which is …
6Compact 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… …
7Moore space (topology) — In mathematics, more specifically point set topology, a Moore space is a developable regular Hausdorff space. Equivalently, a topological space X is a Moore space if the following conditions hold: Any two distinct points can be separated by… …
8Dowker space — A Dowker space is a topological space that is T4 but not countably paracompact. Equivalences If X is a normal T1 space (a T4 space), then the following are equivalent: X is a Dowker space The product of X with the unit interval is not normal. C.… …
9Pseudocompact space — In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded.Conditions for pseudocompactness*Every countably compact space is pseudocompact. For normal… …
10Mesocompact space — In mathematics, in the field of general topology, a topological space is said to be mesocompact if every open cover has a compact finite open refinement.[1] That is, given any open cover, we can find an open refinement with the property that… …
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