A sufficient condition for maximal resolvability of topological spaces

Jerzy Bienias; Małgorzata Terepeta

On resolvable spaces and groups

Luis Miguel Villegas-Silva (1995)

Commentationes Mathematicae Universitatis Carolinae

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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.

Cardinal inequalities implying maximal resolvability

Marek Balcerzak, Tomasz Natkaniec, Małgorzata Terepeta (2005)

Commentationes Mathematicae Universitatis Carolinae

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We compare several conditions sufficient for maximal resolvability of topological spaces. We prove that a space $X$ is maximally resolvable provided that for a dense set $X_{0} \subset X$ and for each $x \in X_{0}$ the $π$ -character of $X$ at $x$ is not greater than the dispersion character of $X$ . On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces.

Displaying similar documents to “A sufficient condition for maximal resolvability of topological spaces”

On resolvable spaces and groups

Cardinal inequalities implying maximal resolvability