| 关于几乎拓扑群的注记 |
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| 引用本文： | 刘鑫,林福财,刘川.关于几乎拓扑群的注记[J].数学研究及应用,2015,35(1):85-91. |
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| 作者姓名： | 刘鑫 林福财 刘川 |
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| 作者单位： | 闽南师范大学数学与统计学院, 福建 漳州 363000;闽南师范大学数学与统计学院, 福建 漳州 363000;俄亥俄大学曾斯维尔分校数学系, 美国 曾斯维尔 OH 43071 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11201414;11471153),福建省自然科学基金(Grant No.2012J05013),福建省高校杰出青年人才培育计划(Grant No.JA13190),福建省中青年教师教育科研项目(Grant No.JA14200). |
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| 摘 要： | 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 π-character is submetrizable;(2) Each left λ-narrow almost topological group isλ-narrow;(3) Each separable almost topological group is ω-narrow. Some questions are posed.
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| 关 键 词： | almost topological group submetrizable λ-narrow separable |
| 收稿时间： | 2014/5/10 0:00:00 |
| 修稿时间： | 2014/9/10 0:00:00 |
A Note on Almost Topological Groups |
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| Xin LIU,Fucai LIN and Chuan LIU.A Note on Almost Topological Groups[J].Journal of Mathematical Research with Applications,2015,35(1):85-91. |
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| Authors: | Xin LIU Fucai LIN and Chuan LIU |
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| Institution: | School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China;School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China;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. |
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| Keywords: | almost topological group submetrizable $\lambda$-narrow separable |
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