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On Lower and Semi-Lower Density Operators

On Lower and Semi-Lower Density Operators This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ -algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On Lower and Semi-Lower Density Operators

Hejduk, Jacek; Loranty, Anna
Georgian Mathematical Journal , Volume 14 (4) – Dec 1, 2007
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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2007.661
Publisher site
See Article on Publisher Site

Abstract

This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ -algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Dec 1, 2007

Keywords: Lower density operator; density topology; topology generated by lower density operator; sets having the Baire property

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