About H-bounded Topological Groups
DOI:
https://doi.org/10.58649/cp41kt60Keywords:
topological group, uniform space, cover, H-boundedness, ω-boundedness, totally boundedness, homomorphism, uniformly continuous mappingAbstract
Although the theory of uniform spaces is independent, it is closely related to the theory of topological groups and there is a profound analogy between them. Therefore, research into the theory of topological groups using uniform structures is relevant.
In this paper some important properties of the H-bounded topological group using uniformities are investigated. In particular, it is established that under precompact continuous homomorphism, the H-bounded property is preserved both in the image and the preimage direction, also the Raikov ℵ0-completion of a H-bounded topological group is H-bounded.
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