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

Constancio Hernández

Mexico

Universidad Autónoma Metropolitana

Dpto. de Matemáticas

D. Robbie

Australia

University of Melbourne

Department of MAthematics and Statistics

Mikhail Tkachenko

Mexico

Universidad Autónoma Metropolitana

Dpto. de Matemáticas
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Accepted: 2014-05-27

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Published: 2000-10-01

DOI: https://doi.org/10.4995/agt.2000.3022
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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.

 

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