2015/07/20 by Fucai Lin, Chuan Liu, Lin, Fucai +1
Mathematics · #54E99 #54H99 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #primary 22A30 #secondary 54D10
paper · pdf · doi:10.48550/arxiv.1507.05646
openalex publication_date 2015/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let FP(X) be the free paratopological group over a topological space X. For each non-negative 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\bigoplus X-1\bigoplus\e\)n to FPn(X). In this paper, we mainly improve some results of A.S. Elfard and P. Nickolas's [On the topology of free paratopological groups. II, Topology Appl., 160(2013), 220--229.]. The main result is that the natural mapping i2: (X\bigoplus Xd-1\bigoplus\e\)2\longrightarrow FP2(X) is a closed mapping if and only if every neighborhood U of the diagonal Δ1 in Xd× 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.