Metrizability of paratopological (semitopological) groups |
| |
Authors: | Chuan Liu |
| |
Institution: | Department of Mathematics, Ohio University Zanesville Campus, Zanesville, OH 43701, USA |
| |
Abstract: | We investigate some generalized metric space properties on paratopological (semitopological) groups and prove that a paratopological group that is quasi-metrizable by a left continuous, left-invariant quasi-metric is a topological group and give a negative answer to Ravsky?s question (Ravsky, 2001 18, Question 3.1]). It is also shown that an uncountable paratopological group that is a closed image of a separable, locally compact metric space is a topological group. Finally, we discuss Hausdorff compactification of paratopological (semitopological) groups, give an affirmative answer to Lin and Shen?s question (Lin and Shen, 2011 14, Question 6.9]) and improve an Arhangel?skii and Choban?s theorem. Some questions are posed. |
| |
Keywords: | 54E35 54E20 54H11 22A05 |
本文献已被 ScienceDirect 等数据库收录! |
|