On hereditarily normal topological groups

"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 -