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Keywords:
one-side porosity; local strong upper porosity; completely strongly porous set; ideal
one-side porosity; local strong upper porosity; completely strongly porous set; ideal
Summary:
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 $\boldsymbol {I}\subseteq \rm SP$. 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).
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