On Ψω-factorizable groups

A topological group G is called Ψω-factorizable (resp. M-factorizable) if every continuous real-valued function on G admits a factorization via a continuous homomorphism onto a topological group H with ψ(H)≤ω (resp. a first-countable group). The first purpose of this article is to discuss some chara...

Full description

Saved in:
Bibliographic Details
Published in:Topology and its applications 2024-12, Vol.358, Article 109129
Main Authors: Zhang, Heng, Xi, Wenfei, Wu, Yaoqiang, Li, Hongling
Format: Article
Language:English
Subjects:
[formula omitted]-factorizable groups
[formula omitted]-uniformly continuous functions
Pseudo-τ-fine
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A topological group G is called Ψω-factorizable (resp. M-factorizable) if every continuous real-valued function on G admits a factorization via a continuous homomorphism onto a topological group H with ψ(H)≤ω (resp. a first-countable group). The first purpose of this article is to discuss some characterizations of Ψω-factorizable groups. It is shown that a topological group G is Ψω-factorizable if and only if every continuous real-valued function on G is Gδ-uniformly continuous, if and only if for every cozero-set U of G, there exists a Gδ-subgroup N of G such that UN=U. Sufficient conditions on the Ψω-factorizable group G to be M-factorizable are that G is τ-fine and τ-steady for a cardinal τ.
ISSN:0166-8641
DOI:10.1016/j.topol.2024.109129