A few generalized metric properties on free paratopological groups

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• 作者：Zhangyong Cai^a ; ^b ; ^{zycaigxu2002@126.com" class="auth_mail" title="E-mail the corresponding author} ; Shou Lin^c ; ^d ; ^{shoulin60@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：22A30 ; 54H99 ; 54D50 ; 54D99 ; 54E18 ; 54E99
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：204
• 期：Complete
• 页码：90-102
• 全文大小：392 K

文摘

In this paper, some generalized metric properties on free paratopological groups are obtained. At first, a general stability theorem of free paratopological groups on submetrizable spaces is established. Secondly, countable tightness of free paratopological groups on k^⁎$k^{⁎}$-metrizable k-spaces or k-semistratifiable k-spaces is investigated. Finally, first-countability of free paratopological groups is discussed and strongly Fréchetness of free paratopological groups is characterized. These complement and improve some known conclusions in literature. In addition, some questions are posed.