On paratopological groups

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• 作者：Fucai Lin^a ; ^{linfucai2008@yahoo.com.cn} ; Chuan Liu^b ; ^{liuc1@ohio.edu}
• 关键词：54E20 ; 54E35 ; 54H11 ; 22A05
• 刊名：Topology and its Applications
• 出版年：2012
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：15 June-1 July, 2012
• 卷：159
• 期：10-11
• 页码：2764-2773
• 文件大小：192 K

摘要

In this paper, we firstly construct a Hausdorff non-submetrizable paratopological group G in which every point is a -set, which gives a negative answer to Arhangel始ski谋虒 and Tkachenko始s question [A.V. Arhangel始ski谋虒, M. Tkachenko, Topological Groups and Related Structures, Atlantis Press and World Sci., 2008]. We also prove that each first-countable Abelian paratopological group is submetrizable. Moreover, we discuss developable paratopological groups and construct a non-metrizable, separable, Moore paratopological group. Further, we prove that a regular, countable, locally -paratopological group is a discrete topological group or contains a closed copy of . Finally, we discuss some properties on non-H-closed paratopological groups, and show that Sorgenfrey line is not H-closed, which gives a negative answer to Arhangel始ski谋虒 and Tkachenko始s question [A.V. Arhangel始ski谋虒, M. Tkachenko, Topological Groups and Related Structures, Atlantis Press and World Sci., 2008]. Some questions are posed.