Some properties of o-bounded and strictly o-bounded groups
Submitted: 2014-05-27
|Accepted: 2014-05-27
|Published: 2000-10-01
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Keywords:
o-bounded group, Strictly o-bounded group, Comfort-like group
Supporting agencies:
Consejo Nacional de Ciencia y Tecnología (CONACYT) de México
grant 400200-5-28411-E
Abstract:
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.
