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In quest of weaker connected topologies. (English) Zbl 0886.54034
The authors study when a topological space has a weaker connected topology. They give various sufficient and necessary conditions for a space to have a weaker Hausdorff or regular connected topology. They prove that the property “space has a weaker Hausdorff or regular connected topology” is preserved by any of the free topological group functors. Examples show that this property is not preserved by “nice” continuous mappings. The paper contains a long list of open problems.
Reviewer: J.Smítal (Opava)

MSC:
54H11 Topological groups (topological aspects)
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
22A05 Structure of general topological groups
54D05 Connected and locally connected spaces (general aspects)
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