On local compactness of the subspace FP₂(X) of FP(X)

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• 作者：Zhangyong Cai^a ; ^b ; ^{zycaigxu2002@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：22A30 ; 54B05 ; 54C20 ; 54D45 ; 54E15
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：197
• 期：Complete
• 页码：181-188
• 全文大小：294 K

文摘

In this paper, it is shown that if X is homeomorphic to the topological sum of a Tychonoff space Y and a discrete space D  , then FP₂(X)$F{P}_2(X)$ is locally compact if and only if FP₂(Y)$F{P}_2(Y)$ is locally compact. Especially, the space FP₂(X)$F{P}_2(X)$ is locally compact at its every point distinct from the identity e if X is homeomorphic to the topological sum of a compact space and a discrete space. Finally, a few questions about free paratopological groups are posed.