Some properties of o-bounded and strictly o-bounded groups

C. Hernández, Mikhail Tkachenko, D. Robbie


We continue the study of (strictly) o-bounded topological groups initiated by the first listed author and solve two problems posed earlier. It is shown here that the product of a Comfort-like topological group by a (strictly) o-bounded group is (strictly) o-bounded. Some non-trivial examples of strictly o-bounded free topological groups are given. We also show that o-boundedness is not productive, and strict o-boundedness cannot be characterized by means of second countable continuous homomorphic images.



o-bounded group ; Strictly o-bounded group ; Comfort-like group

Subject classification

54H11; 22A05; 22D05; 54C50

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1. The character of free topological groups II
Peter Nickolas, Mikhail Tkachenko
Applied General Topology  vol: 6  issue: 1  first page: 43  year: 2005  
doi: 10.4995/agt.2005.1962

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147