Geodesic
In quest of weaker connected topologies
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 825-841
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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 is rather strong, but we show that it is difficult to construct spaces which would contain no infinite subspaces with a weaker connected $T_{3{1\over 2}}$-topology.
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 is rather strong, but we show that it is difficult to construct spaces which would contain no infinite subspaces with a weaker connected $T_{3{1\over 2}}$-topology.
Classification : 22A05, 54C10, 54C25, 54D05, 54D06, 54D10, 54D25, 54H11
Keywords: connected; locally connected; free topological group; condensation; connectification 
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     author = {Tka\v{c}enko, M. G. and Tkachuk, V. V. and Uspenskii, V. V. and Wilson, R. G.},
     title = {In quest of weaker connected topologies},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {825--841},
     year = {1996},
     volume = {37},
     number = {4},
     mrnumber = {1440714},
     zbl = {0886.54034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996_37_4_a15/}
}
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Tkačenko, M. G.; Tkachuk, V. V.; Uspenskii, V. V.; Wilson, R. G. In quest of weaker connected topologies. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 825-841. http://geodesic.mathdoc.fr/item/CMUC_1996_37_4_a15/