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On cellular-compact spaces.
- Source :
-
Acta Mathematica Hungarica . Dec2020, Vol. 162 Issue 2, p549-556. 8p. - Publication Year :
- 2020
-
Abstract
- As it was introduced by Tkachuk and Wilson in [7], a topological space X is cellular-compact if for any cellular, i.e. disjoint, family U of non-empty open subsets of X there is a compact subspace K ⊂ X such that K ∩ U ≠ ∅ for each U ∈ U . In this note we answer several questions raised in [7] by showing that any first countable cellular-compact T2-space is T3, and so its cardinality is at most c = 2 ω ; cov (M) > ω 1 implies that every first countable and separable cellular-compactT2-space is compact; if there is no S-space then any cellular-compact T3-space of countable spread is compact; M A ω 1 implies that every point of a compact T2-space of countable spread has a disjoint local π -base. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMPACT spaces (Topology)
*MERGERS & acquisitions
*TOPOLOGICAL spaces
*SPACE
Subjects
Details
- Language :
- English
- ISSN :
- 02365294
- Volume :
- 162
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Hungarica
- Publication Type :
- Academic Journal
- Accession number :
- 146931331
- Full Text :
- https://doi.org/10.1007/s10474-020-01035-4