On Hereditarily Normal Topological Groups
General Topology
2012-09-11 v2
Abstract
In this paper we investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has -diagonal. This implies, in particular, that every countably compact subset of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary is that under the Proper Forcing Axiom, every countably compact subset of a hereditarily normal topological group is metrizable.
Cite
@article{arxiv.1209.0847,
title = {On Hereditarily Normal Topological Groups},
author = {Raushan Buzyakova},
journal= {arXiv preprint arXiv:1209.0847},
year = {2012}
}