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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 2004
- DOI:
- 10.48550/arXiv.math/0402236
- arXiv:
- arXiv:math/0402236
- Bibcode:
- 2004math......2236L
- Keywords:
-
- Mathematics - General Topology;
- Mathematics - Category Theory;
- Mathematics - Group Theory;
- 22A05;
- 22C05 (Primary) 54D30 (Secondary)
- E-Print:
- 12 pages