Two ideals connected with strong right upper porosity at a point

Viktoriia Bilet; Oleksiy Dovgoshey; Jürgen Prestin

doi:10.1007/s10587-015-0204-3

Two ideals connected with strong right upper porosity at a point

Viktoriia Bilet^*, Oleksiy Dovgoshey, Jürgen Prestin

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Mathematik

1 Zitat (Scopus)

Abstract

Let SP be the set of upper strongly porous at 0 subsets of ℝ⁺ and let Î(SP) be the intersection of maximal ideals I ⊆ SP. Some characteristic properties of sets E ∈ Î(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of ℝ⁺ is a proper subideal of Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014).

Originalsprache	Englisch
Zeitschrift	Czechoslovak Mathematical Journal
Jahrgang	65
Ausgabenummer	3
Seiten (von - bis)	713-737
Seitenumfang	25
ISSN	0011-4642
DOIs	https://doi.org/10.1007/s10587-015-0204-3
Publikationsstatus	Veröffentlicht - 01.09.2015

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10.1007/s10587-015-0204-3

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abstract = "Let SP be the set of upper strongly porous at 0 subsets of ℝ+ and let {\^I}(SP) be the intersection of maximal ideals I ⊆ SP. Some characteristic properties of sets E ∈ {\^I}(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of ℝ+ is a proper subideal of {\^I}(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014).",

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AU - Bilet, Viktoriia

AU - Dovgoshey, Oleksiy

AU - Prestin, Jürgen

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N2 - Let SP be the set of upper strongly porous at 0 subsets of ℝ+ and let Î(SP) be the intersection of maximal ideals I ⊆ SP. Some characteristic properties of sets E ∈ Î(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of ℝ+ is a proper subideal of Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014).

AB - Let SP be the set of upper strongly porous at 0 subsets of ℝ+ and let Î(SP) be the intersection of maximal ideals I ⊆ SP. Some characteristic properties of sets E ∈ Î(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of ℝ+ is a proper subideal of Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014).

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EP - 737

JO - Czechoslovak Mathematical Journal

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