Title: Notes on remainders of topological spaces in some compactifications
Abstract: In this paper, we investigate the compactifications of some topological spaces such that their remainders have countable tightness. We also study addition theorems for compacta. The main results are: (1) If bX is a compactification of a first-countable space X with a Gδ-diagonal (or a space X with a point-countable base) and bX∖X has countable tightness, then both bX and bX∖X have countable fan-tightness; (2) If a non-locally compact paratopological group G has a compactification bG such that the remainder bG∖G is the union of a finite family of metrizable subspaces, then G is locally separable and locally metrizable; (3) If a compact Hausdorff space Z=X∪Y, where X is a non-locally compact topological group which is a σ-space and dense in Z, and Y is a semitopological group, then Z is separable and metrizable; (4) If a compact Hausdorff space Z=X∪Y, where X is a non-locally compact paratopological group that has a countable network and is dense in Z, and Y is a semitopological group, then Z is separable and metrizable. Among them (2) and (3) improve the corresponding results given by A.V. Arhangel'skii in [7].
Publication Year: 2016
Publication Date: 2016-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 1
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