Open AccessSome properties of o-bounded and strictly o-bounded groups
Author(s) -
Constancio Hernández,
Mikhail Tkachenko,
Desmond A. Robbie
Publication year - 2000
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2000.3022
Subject(s) - bounded function , mathematics , countable set , group (periodic table) , discrete mathematics , pure mathematics , combinatorics , topology (electrical circuits) , mathematical analysis , chemistry , organic chemistry
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