| A Note on Almost Topological Groups |
| Received:May 10, 2014 Revised:September 10, 2014 |
| Key Words:
almost topological group submetrizable $\lambda$-narrow separable
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11201414; 11471153), the Natural Science Foundation of Fujian Province (Grant No.2012J05013), the Training Programme Foundation for Excellent Youth Researching Talents of Fujian's Universities (Grant No.\,JA13190) and the Foundation of the Education Department of Fujian Province (Grant No.JA14200). |
| Author Name | Affiliation | | Xin LIU | School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China | | Fucai LIN | School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China | | Chuan LIU | Department of Mathematics, Ohio University Zanesville Campus, Zanesville, OH 43701, USA |
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| Abstract: |
| In this paper, we mainly discuss some generalized metric properties and the cardinal invariants of almost topological groups. We give a characterization for an almost topological group to be a topological group and show that: (1) Each almost topological group that is of countable $\pi$-character is submetrizable; (2) Each left $\lambda$-narrow almost topological group is $\lambda$-narrow; (3) Each separable almost topological group is $\omega$-narrow. Some questions are posed. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.01.007 |
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