Displaying similar documents to “A note on countable connected locally connected Urysohn almost regular spaces”

Open subspaces of countable dense homogeneous spaces

Stephen Watson, Petr Simon (1992)

Fundamenta Mathematicae

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We construct a completely regular space which is connected, locally connected and countable dense homogeneous but not strongly locally homogeneous. The space has an open subset which has a unique cut-point. We use the construction of a C 1 -diffeomorphism of the plane which takes one countable dense set to another.

In quest of weaker connected topologies

Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Vladimir Vladimirovich Uspenskij, Richard Gordon Wilson (1996)

Commentationes Mathematicae Universitatis Carolinae

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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...