A Note on Almost Topological Groups
Received:May 10, 2014  Revised:September 10, 2014
Key Word: almost topological group   submetrizable   $\lambda$-narrow   separable
Fund ProjectL: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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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.