| 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
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.12171015; 62272015). |
| Author Name | Affiliation | | 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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