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

[EN] 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.The research is partially supported by Consejo Nacional de Ciencias y Tecnología (CONACyT) of Mexico, grant no. 400200-5-28411E, and grant for Special Studies Program (Long) The University of Melbourne (Science Faculty).Hernández, C.; Robbie, D.; Tkachenko, M. (2000). Some properties of o-bounded and strictly o-bounded groups. Applied General Topology. 1(1):29-43. doi:10.4995/agt.2000.3022SWORD29431