On Ψω-factorizable groups

A topological group G is called Psi w-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 psi ( H ) <= omega (resp. a first-countable group). The first purpose of this article is to discuss some characterizations of Psi w- factorizable groups. It is shown that a topological group G is Psi w-factorizable if and only if every continuous real-valued function on G is G s-uniformly continuous, if and only if for every cozero-set U of G , there exists a G s-subgroup N of G such that UN = U . Sufficient conditions on the Psi w-factorizable group G to be M-factorizable are that G is tau-fine and tau-steady for a cardinal tau . (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.