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

^*Corresponding author for this work

Institute of Mathematics

1 Citation (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).

Original language	English
Journal	Czechoslovak Mathematical Journal
Volume	65
Issue number	3
Pages (from-to)	713-737
Number of pages	25
ISSN	0011-4642
DOIs	https://doi.org/10.1007/s10587-015-0204-3
Publication status	Published - 01.09.2015

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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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T1 - Two ideals connected with strong right upper porosity at a point

AU - Bilet, Viktoriia

AU - Dovgoshey, Oleksiy

AU - Prestin, Jürgen

PY - 2015/9/1

Y1 - 2015/9/1

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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U2 - 10.1007/s10587-015-0204-3

DO - 10.1007/s10587-015-0204-3

M3 - Journal articles

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SN - 0011-4642

VL - 65

SP - 713

EP - 737

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

IS - 3

ER -

Two ideals connected with strong right upper porosity at a point

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