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arXiv · 1209.0847

On Hereditarily Normal Topological Groups

Raushan Buzyakova
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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 $G_δ$-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.

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Raushan Buzyakova. 2012-09-10. On Hereditarily Normal Topological Groups. https://arxiv.org/abs/1209.0847

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