On sequentially h-complete groups

Gábor Lukács

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arXiv · math/0210354

On sequentially h-complete groups

Gábor Lukács

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Abstract

A topological group $G$ is {\em sequentially $h$-complete} if all the continuous homomorphic images of $G$ are sequentially complete. In this paper we give necessary and sufficient conditions on a complete group for being compact, using the language of sequential $h$-completeness. In the process of obtaining such conditions, we establish a structure theorem for $ω$-precompact sequentially $h$-complete groups. As a consequence we obtain a reduction theorem for the problem of $c$-compactness.

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Gábor Lukács. 2004-01-15. On sequentially h-complete groups. https://arxiv.org/abs/math/0210354

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