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RESOLVABILITY PROPERTIES OF SIMILAR TOPOLOGIES

Part of: Classical measure theory Sequences and sets Generalities

Published online by Cambridge University Press:  03 September 2015

SEBASTIAN LINDNER
SEBASTIAN LINDNER*
Affiliation:
Department of Mathematics and Computer Science, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland email lindner@math.uni.lodz.pl
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Abstract

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We demonstrate that many properties of topological spaces connected with the notion of resolvability are preserved by the relation of similarity between topologies. Moreover, many of them can be characterised by the properties of the algebra of sets with nowhere dense boundary and the ideal of nowhere dense sets. We use these results to investigate whether a given pair of an algebra and an ideal is topological.

Keywords

resolvabilitynowhere dense setssemi-open setssemi-correspondencedensity topologysimilar topologies

MSC classification

Primary: 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
Secondary: 54A05: Topological spaces and generalizations (closure spaces, etc.) 11B05: Density, gaps, topology 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 470 - 477
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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