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- W2073644511 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 $G_delta$-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." @default.
- W2073644511 created "2016-06-24" @default.
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- W2073644511 date "2012-09-05" @default.
- W2073644511 modified "2023-09-27" @default.
- W2073644511 title "On Hereditarily Normal Topological Groups" @default.
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