Open AccessMapping i2 on the free paratopological groups
Author(s) -
Fucai Lin,
Chuan Liu
Publication year - 2017
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim1715213l
Subject(s) - diagonal , space (punctuation) , topology (electrical circuits) , topological space , integer (computer science) , mathematics , combinatorics , discrete space , natural number , discrete mathematics , computer science , geometry , mathematical analysis , programming language , operating system
Let FP(X) be the free paratopological group over a topological space X. For each nonnegative integer n ? N, denote by FPn(X) the subset of FP(X) consisting of all words of reduced length at most n, and in by the natural mapping from (X ? X?1 ? {e})n to FPn(X). We prove that the natural mapping i2:(X ? X?1 d ?{e})2 ? FP2(X) is a closed mapping if and only if every neighborhood U of the diagonal ?1 in Xd x X is a member of the finest quasi-uniformity on X, where X is a T1-space and Xd denotes X when equipped with the discrete topology in place of its given topology.