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On resolvable spaces and groups

Luis Miguel Villegas-Silva (1995)

Commentationes Mathematicae Universitatis Carolinae

It is proved that every uncountable ω -bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.

On some classes of spaces with the D -property

Juan Carlos Martínez (2014)

Commentationes Mathematicae Universitatis Carolinae

We shall prove that under CH every regular meta-Lindelöf P -space which is locally D has the D -property. In addition, we shall prove that a regular submeta-Lindelöf P -space is D if it is locally D and has locally extent at most ω 1 . Moreover, these results can be extended from the class of locally D -spaces to the wider class of 𝔻 -scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology...

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