Two ideals connected with strong right upper porosity at a point

Viktoriia Bilet; Oleksiy Dovgoshey; Jürgen Prestin

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 3, page 713-737
  • ISSN: 0011-4642

Abstract

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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).

How to cite

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Bilet, Viktoriia, Dovgoshey, Oleksiy, and Prestin, Jürgen. "Two ideals connected with strong right upper porosity at a point." Czechoslovak Mathematical Journal 65.3 (2015): 713-737. <http://eudml.org/doc/271821>.

@article{Bilet2015,
abstract = {Let $\rm SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb \{R\}^\{+\}$ and let $\hat\{I\}(\rm SP)$ be the intersection of maximal ideals $I\subseteq \rm SP$. Some characteristic properties of sets $E\in \hat\{I\}(\rm SP)$ 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 $\mathbb \{R\}^\{+\}$ is a proper subideal of $\hat\{I\}(\rm SP).$ Earlier, completely strongly porous sets and some of their properties were studied in the paper V. Bilet, O. Dovgoshey (2013/2014).},
author = {Bilet, Viktoriia, Dovgoshey, Oleksiy, Prestin, Jürgen},
journal = {Czechoslovak Mathematical Journal},
keywords = {one-side porosity; local strong upper porosity; completely strongly porous set; ideal},
language = {eng},
number = {3},
pages = {713-737},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two ideals connected with strong right upper porosity at a point},
url = {http://eudml.org/doc/271821},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Bilet, Viktoriia
AU - Dovgoshey, Oleksiy
AU - Prestin, Jürgen
TI - Two ideals connected with strong right upper porosity at a point
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 713
EP - 737
AB - Let $\rm SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb {R}^{+}$ and let $\hat{I}(\rm SP)$ be the intersection of maximal ideals $I\subseteq \rm SP$. Some characteristic properties of sets $E\in \hat{I}(\rm SP)$ 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 $\mathbb {R}^{+}$ is a proper subideal of $\hat{I}(\rm SP).$ Earlier, completely strongly porous sets and some of their properties were studied in the paper V. Bilet, O. Dovgoshey (2013/2014).
LA - eng
KW - one-side porosity; local strong upper porosity; completely strongly porous set; ideal
UR - http://eudml.org/doc/271821
ER -

References

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