Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

Streszczenie

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 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.