On the separation axioms of topologies generatedby regular sequences of measurable sets

Authors

  • Mikołaj Widzibor Faculty of Mathematics and Computer Science, University of Łódź, Poland

Keywords:

lower density operator, topology generated by lower density operator, density topology

Abstract

In this paper we study separation axioms for S-density topology, which is a generalization of the classical density topology. Namely, we prove that if the sequence of sets is regular, then the topology generated by it is completely regular, but is not normal.

References

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J. Hejduk, A. Loranty, On abstract and almost-abstract density topologies, Acta Math. Hungar. 155(2) (2018), 228–240.

J. Hejduk, R. Wiertelak, On some properties of J -approximately continuous functions, Math. Slovaca 67(6) (2017), 1–10.

J. Hejduk, R. Wiertelak, On the abstract density topologies generated by lower and almost lower density operators, Traditional and present-day topics in real analysis, Łódź University Press, 2013.

F. Strobin, R. Wiertelak, On a generalization of density topologies on the real line, Topology Appl. 199 (2016), 1–16.

M. Widzibor, R.Wiertelak, On properties of operators generated by regular sequences of measurable sets, submitted, (2018).

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Published

2020-10-01

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Articles