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- W4297445993 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.
- W4297445993 created "2022-09-28" @default.
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- W4297445993 date "2012-09-04" @default.
- W4297445993 modified "2023-09-29" @default.
- W4297445993 title "On Hereditarily Normal Topological Groups" @default.
- W4297445993 doi "https://doi.org/10.48550/arxiv.1209.0847" @default.
- W4297445993 hasPublicationYear "2012" @default.
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