# In quest of weaker connected topologies

Mihail G. Tkachenko; Vladimir Vladimirovich Tkachuk; Vladimir Vladimirovich Uspenskij; Richard Gordon Wilson

Commentationes Mathematicae Universitatis Carolinae (1996)

- Volume: 37, Issue: 4, page 825-841
- ISSN: 0010-2628

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topTkachenko, Mihail G., et al. "In quest of weaker connected topologies." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 825-841. <http://eudml.org/doc/247940>.

@article{Tkachenko1996,

abstract = {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.},

author = {Tkachenko, Mihail G., Tkachuk, Vladimir Vladimirovich, Uspenskij, Vladimir Vladimirovich, Wilson, Richard Gordon},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {connected; locally connected; free topological group; condensation; connectification; connected; locally connected; free topological group; condensation; connectification},

language = {eng},

number = {4},

pages = {825-841},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {In quest of weaker connected topologies},

url = {http://eudml.org/doc/247940},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Tkachenko, Mihail G.

AU - Tkachuk, Vladimir Vladimirovich

AU - Uspenskij, Vladimir Vladimirovich

AU - Wilson, Richard Gordon

TI - In quest of weaker connected topologies

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1996

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 37

IS - 4

SP - 825

EP - 841

AB - 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.

LA - eng

KW - connected; locally connected; free topological group; condensation; connectification; connected; locally connected; free topological group; condensation; connectification

UR - http://eudml.org/doc/247940

ER -

## References

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