In quest of weaker connected topologies
Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Vladimir Vladimirovich Uspenskij, Richard Gordon Wilson (1996)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We study when a topological space has a weaker connected topology. Various sufficient and necessary conditions are given for a space to have a weaker Hausdorff or regular connected topology. It is proved that the property of a space of having a weaker Tychonoff topology is preserved by any of the free topological group functors. Examples are given for non-preservation of this property by “nice” continuous mappings. The requirement that a space have a weaker Tychonoff connected topology...