EMIS ELibM Electronic Journals Publications de l’Institut Mathématique, Nouvelle Série
Vol. 101[115], pp. 213–221 (2017)

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Fucai Lin, Chuan Liu

School of mathematics and statistics, Minnan Normal University, Zhangzhou, P. R. China; Department of Mathematics, Ohio University Zanesville Campus, Zanesville, USA

Abstract: Let FP(X) be the free paratopological group over a topological space X. For each nonnegative integer n, denote by FP n (X) the subset of FP(X) consisting of all words of reduced length at most n, and i n by the natural mapping from (XX -1 {e}) n to FP n (X). We prove that the natural mapping i 2 :(XX d -1 {e}) 2 FP 2 (X) is a closed mapping if and only if every neighborhood U of the diagonal Δ 1 in X d ×X is a member of the finest quasi-uniformity on X, where X is a T 1 -space and X d denotes X when equipped with the discrete topology in place of its given topology.

Keywords: free paratopological groups; quotient mappings; closed mappings; finest quasi-uniformity

Classification (MSC2000): 22A30; 54D10; 54E99; 54H99

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Electronic fulltext finalized on: 24 Apr 2017. This page was last modified: 11 May 2017.

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