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...

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

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

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

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

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

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

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...