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On θ -closed sets and some forms of continuity

Mohammad Saleh (2004)

Archivum Mathematicum

In this paper, we further the study of θ -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using θ -open and δ -open sets. Among other results, it is shown a weakly θ -retract of a Hausdorff space X is a δ -closed subset of X .

Open subspaces of countable dense homogeneous spaces

Stephen Watson, Petr Simon (1992)

Fundamenta Mathematicae

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.

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