Open subgroups of free topological groups

• Autorzy: Jeremy Brazas
• Języki publikacji: EN

Abstrakty

EN

The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.

Kategorie tematyczne

• 55R65: Generalizations of fiber spaces and bundles
• 55Q52: Homotopy groups of special spaces
• 22A05: Structure of general topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 226
• Numer: 1
• Strony: 17-40

Daty

wydano

2014

Twórcy

autor

Jeremy Brazas

• Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, U.S.A.

Identyfikatory

DOI

10.4064/fm226-1-2