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Comparison of ψ-porous topologies

  • Ewa Łazarow EMAIL logo , Krystian Rychert and Małgorzata Turowska
From the journal Mathematica Slovaca

Abstract

The purpose of this paper is to study the notion of a ψ-porosity point and ψ-porosity topology, generated by it analogously to the porosity topology on the real line. The paper includes a necessary and sufficient conditions under which two ψ-porous topologies generated by two functions ψ1 and ψ2 are equal. The condition is formulated in terms of the behavior of two sequences of sets Ak={x(0,):ψ1(x)<1kψ2(x)} and Bk={x(0,):ψ2(x)<1kψ1(x)}.

MSC 2010: Primary 26A15; 54A10

(Communicated by Ľubica Holá)


References

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Received: 2015-7-1
Accepted: 2015-11-12
Published Online: 2017-7-14
Published in Print: 2017-8-28

© 2017 Mathematical Institute Slovak Academy of Sciences

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