Dense subgroups of paratopological groups

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• 作者：Ivá ; n Sá ; nchez ^{isr.uami@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：54D10 ; 54B30 ; 54C10 ; 54H99
• 刊名：Topology and its Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：196
• 期：part_PA
• 页码：241-248
• 全文大小：282 K

文摘

We show that if H   is a dense subgroup of a T₃$T_3$ semitopological group G such that H is a paratopological group, then G is a paratopological group as well. Also, we prove that a semitopological group G is a topological group provided G   is T₃$T_3$ and it contains a dense topological subgroup.

We show that the functors T₃$T_3$ and Reg(G)$\mathit{Reg}(G)$ do not respect dense subgroups of semitopological groups. This answers a problem posed by Mikhail Tkachenko.