1. Some characterizations of ω-balanced topological groups with a <italic>q</italic>-point.
- Author
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Chen, Deng-Bin, Lin, Hai-Hua, and Xie, Li-Hong
- Abstract
AbstractIn this paper, we study some characterizations of
q -spaces, strictq -spaces and strongq -spaces underω -balanced topological groups. First we characterize a topological groupG to beω -balanced and aq -space whenever for each open neighborhoodO of the identity inG , there is a countably compact invariant subgroupH which is of countable character inG , such thatH ⊆O and the canonical quotient mappingp :G →G/H is quasi-perfect and the quotient groupG/H is metrizable. Secondly, we characterizeG to beω -balanced and a strictq -space, replacing the condition of being aq -space with an appropriate condition which is designed for the so-called “strictq -spaces”. Finally, we characterizeG to beω -balanced and a strongq -space, illustrating an additional condition to be replaced to that ofq -space, or strictq -space. As applications of our three main results, we found new characterizations of theω -narrow topological groups. [ABSTRACT FROM AUTHOR]- Published
- 2024
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