Hereditarily hcomplete groups
Abstract
A topological group G is hcomplete if every continuous homomorphic image of G is (Raikov)complete; we say that G is hereditarily hcomplete if every closed subgroup of G is hcomplete. In this paper, we establish openmap properties of hereditarily hcomplete 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 hcomplete group with quasiinvariant basis is the projective limit of its metrizable quotients; 2. If every countable discrete hereditarily hcomplete group is finite, then every locally compact hereditarily hcomplete group that has small invariant neighborhoods is compact. In the sequel, several open problems are formulated.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402236
 Bibcode:
 2004math......2236L
 Keywords:

 Mathematics  General Topology;
 Mathematics  Category Theory;
 Mathematics  Group Theory;
 22A05;
 22C05 (Primary) 54D30 (Secondary)
 EPrint:
 12 pages