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...
3 KB (340 words) - 13:40, 23 December 2021
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...
23 KB (3,481 words) - 18:27, 16 June 2024
generated space Compactness theorem Eberlein compactum Exhaustion by compact sets Lindelöf space Metacompact space Noetherian topological space Orthocompact...
45 KB (5,681 words) - 09:54, 31 July 2024
preserving. Hence, we have the following: every metacompact space, and in particular, every paracompact space, is orthocompact. Useful theorems: Orthocompactness...
2 KB (262 words) - 10:30, 10 June 2024
483-496, 1966. [2] Compact space Paracompact space Normal space Realcompact space Metacompact space Orthocompact space Tychonoff space Engelking, Ryszard (1968)...
6 KB (611 words) - 19:39, 4 December 2022
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...
1 KB (182 words) - 19:53, 17 June 2024
Carathéodory's extension theorem Geometric set cover problem Dimension theory Metacompact space Point-finite collection Lebesgue, Henri (1921). "Sur les correspondances...
13 KB (1,475 words) - 02:52, 4 June 2024
compact metacompact space is compact. Every countably compact Hausdorff first-countable space is regular. Every normal countably compact space is collectionwise...
7 KB (558 words) - 04:09, 5 June 2024
Locally finite collection (redirect from Locally finite spaces)
definitions of paracompact space and metacompact space, and this is the reason why every paracompact space is metacompact. If a collection of sets is...
6 KB (984 words) - 04:28, 21 June 2024
Thus, every normal metacompact space is a shrinking space. In particular, every Hausdorff paracompact space is a shrinking space. These facts are particularly...
2 KB (183 words) - 16:09, 16 August 2024