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...

product of a paracompact space and a compact space is paracompact. The product of a metacompact space and a compact space is metacompact. Both these results...

generated space Compactness theorem Eberlein compactum Exhaustion by compact sets Lindelöf space Metacompact space Noetherian topological space Orthocompact...

preserving. Hence, we have the following: every metacompact space, and in particular, every paracompact space, is orthocompact. Useful theorems: Orthocompactness...

483-496, 1966. [2] Compact space Paracompact space Normal space Realcompact space Metacompact space Orthocompact space Tychonoff space Engelking, Ryszard (1968)...

many members of U . {\displaystyle {\mathcal {U}}.} A metacompact space is a topological space in which every open cover admits a point-finite open refinement...

Carathéodory's extension theorem Geometric set cover problem Dimension theory Metacompact space Point-finite collection Lebesgue, Henri (1921). "Sur les correspondances...

compact metacompact space is compact. Every countably compact Hausdorff first-countable space is regular. Every normal countably compact space is collectionwise...

definitions of paracompact space and metacompact space, and this is the reason why every paracompact space is metacompact. If a collection of sets is...

Thus, every normal metacompact space is a shrinking space. In particular, every Hausdorff paracompact space is a shrinking space. These facts are particularly...