On hereditarily normal topological groups

• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 22A05: Structure of general topological groups
• 54H11: Topological groups
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 219
• Numer: 3
• Strony: 245-251

Daty

wydano

2012

Twórcy

Identyfikatory

DOI

10.4064/fm219-3-3