Hereditarily h-complete groups

Details Hereditarily h-complete groups Hereditarily h-complete groups

2004-02-14

arxiv.org/abs/math/0402236v2

Topology and its Applications 145 (2004), no. 1-3, 177-189

Mathematics

General Topology

12 pages; few changes were made compared to the original submission thanks to the suggestions of the referee

Scientific paper

10.1016/j.topol.2004.06.009

A topological group G is h-complete if every continuous homomorphic image of G is (Raikov-)complete; we say that G is hereditarily h-complete if every closed subgroup of G is h-complete. In this paper, we establish open-map properties of hereditarily h-complete groups with respect to large classes of groups, and prove a theorem on the (total) minimality of subdirectly represented groups. Numerous applications are presented, among them: 1. Every hereditarily h-complete group with quasi-invariant basis is the projective limit of its metrizable quotients; 2. If every countable discrete hereditarily h-complete group is finite, then every locally compact hereditarily h-complete group that has small invariant neighborhoods is compact. In the sequel, several open problems are formulated.

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