کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4657892 | 1633071 | 2016 | 9 صفحه PDF | دانلود رایگان |
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 GδGδ-diagonal (or a space X with a point-countable base) and bX∖XbX∖X has countable tightness, then both bX and bX∖XbX∖X have countable fan-tightness; (2) If a non-locally compact paratopological group G has a compactification bG such that the remainder bG∖GbG∖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∪YZ=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∪YZ=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].
Journal: Topology and its Applications - Volume 208, 1 August 2016, Pages 55–63