MP-equivalence of free paratopological groups

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• 作者：Zhangyong Cai^a ; ^{zycaigxu2002@126.com} ; Shou Lin^b ; ^{shoulin60@163.com}
• 关键词：22A30 ; 54C10 ; 54D20 ; 54D65 ; 54E20
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：215
• 期：Complete
• 页码：35-44
• 全文大小：342 K
• 卷排序：215

文摘

Let FP(X)FP(X) denote the free paratopological group over a topological space X. Two topological spaces X and Y are called MP-equivalent   if FP(X)FP(X) and FP(Y)FP(Y) are topologically isomorphic. At first, it is shown that there exist non-homeomorphic topological spaces X and Y   such that FP(X)FP(X) and FP(Y)FP(Y) are topologically isomorphic. Secondly, MP-invariance of free paratopological groups is investigated. It is established that pseudocompactness, hereditary Lindelöfness, hereditary separability and the property of being a cosmic space are all MP-invariant, which generalizes some conclusions valid for free topological groups to free paratopological groups. Finally, a few questions about MP-equivalence of free paratopological groups are posed.