# On hereditarily normal topological groups

Fundamenta Mathematicae (2012)

- Volume: 219, Issue: 3, page 245-251
- ISSN: 0016-2736

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top"On hereditarily normal topological groups." Fundamenta Mathematicae 219.3 (2012): 245-251. <http://eudml.org/doc/283108>.

@article{Unknown2012,

abstract = {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 subspace 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 subspace of a hereditarily normal topological group is metrizable.},

journal = {Fundamenta Mathematicae},

keywords = {topological group; hereditarily normal space},

language = {eng},

number = {3},

pages = {245-251},

title = {On hereditarily normal topological groups},

url = {http://eudml.org/doc/283108},

volume = {219},

year = {2012},

}

TY - JOUR

TI - On hereditarily normal topological groups

JO - Fundamenta Mathematicae

PY - 2012

VL - 219

IS - 3

SP - 245

EP - 251

AB - 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 subspace 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 subspace of a hereditarily normal topological group is metrizable.

LA - eng

KW - topological group; hereditarily normal space

UR - http://eudml.org/doc/283108

ER -

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