On sequentially h-complete groups

Details On sequentially h-complete groups On sequentially h-complete groups

2002-10-22

arxiv.org/abs/math/0210354v3

Galois theory, Hopf algebras and semiabelian categories, Fields Institute Communications 43 (2004), 353-358

Mathematics

Group Theory

v5: Typo correction (Jaunary 15, 2004)

Scientific paper

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 $\omega$-precompact sequentially $h$-complete groups. As a consequence we obtain a reduction theorem for the problem of $c$-compactness.

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