About S-bounded Topological Groups
DOI:
https://doi.org/10.58649/gedwvt34Keywords:
Topological group, uniform space, uniform cover, S-boundednessAbstract
Topological groups and uniform spaces are closely linked through the concept of a uniform structures. Each topological group naturally gives rise to a uniform structure, which makes it possible to extend the concepts of uniform continuity and completion. In this paper S-bounded topological groups are studied using uniform structures, in particular, it is proved that S-boundedness is preserved under continuous homomorphism into the image and that the completion of any S-bonded topological group is a S-bonded topological group.
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No datasets were generated or analysed during the current study.
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Copyright (c) 2026 U.A. Saktanov, B.E. Kanetov (Author)
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