A Note on $Pm$-Factorizable Topological Groups
Received:April 03, 2023  Revised:July 08, 2023
Key Words: $\mathbb{R}$-factorizable   $P\mathbb{R}$-factorizable   $m$-factorizable   $Pm$-factorizable   $\mathcal{M}$-factorizable  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.12171015; 62272015).
Author NameAffiliation
Chunjie MA Department of Mathematics, School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, P. R. China 
Liangxue PENG Department of Mathematics, School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, P. R. China 
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Abstract:
      In this paper, we define a new class of $Pm$-factorizable topological groups. A topological group $G$ is called $Pm$-factorizable if, for every continuous function $f: G\rightarrow M$ to a metrizable space $M$, one can find a perfect homomorphism $\pi: G\rightarrow K$ onto a second-countable topological group $K$ and a continuous function $g: K\rightarrow M$ such that $f=g\circ\pi$. We show that a topological group $G$ is $Pm$-factorizable if and only if it is $P\mathbb{R}$-factorizable. And we get that if $G$ is a $Pm$-factorizable topological group and $K$ is any compact topological group, then the group $G\times K$ is $Pm$-factorizable.
Citation:
DOI:10.3770/j.issn:2095-2651.2024.02.007
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