Year: 2025
Type: article
Abstract: In this article, firstly, we introduce the concepts of weak q-spaces and weak sq-spaces. Some properties of these spaces are discussed. Secondly, we study weak q-spaces and weak sq-spaces in topological groups in terms of preimages of submetrizable spaces. We show that a topological group G is a weak q-space (resp., weak sq-space) if and only if it is an open countable-compact (resp., sequential-compact) preimage of a submetrizable space.Finally, we give some characterizations of weakly feathered, weak q-spaces and weak sq-spaces in topological groups in coset spaces as follows:(1) Let H be a closed neutral subgroup of a topological group G. Then G/H is weakly feathered if and only if G/H is an open perfect preimage of a submetrizable space.(2) Let H be a closed neutral subgroup of a topological group G. Then G/H is a weak q-space (resp., weak sq-space) if and only if G/H is an open countable-compact (resp., sequential-compact) preimage of a submetrizable space.
Source: Applied General Topology
Authors: Hai-Hua Lin, Li-Hong Xie
Institutions: Wuyi University, Wuyi University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: G6036252855, G7296635248
OpenAlex ID: W4414873715