Hereditarily h-complete groups
Abstract
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.
Cite
@article{arxiv.math/0402236,
title = {Hereditarily h-complete groups},
author = {Gábor Lukács},
journal= {arXiv preprint arXiv:math/0402236},
year = {2011}
}
Comments
12 pages; few changes were made compared to the original submission thanks to the suggestions of the referee