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Two ideals connected with strong right upper porosity at a point. (English) Zbl 1363.28001

Summary: Let \(\text{SP}\) be the set of upper strongly porous at \(0\) subsets of \(\mathbb{R}^+\) and let \(\hat{I}(\text{SP})\) be the intersection of maximal ideals \(\pmb{I}\subseteq \text{SP}\). Some characteristic properties of sets \(E\in \hat{I}(\text{SP})\) 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 \(\hat{I}(\text{SP}).\) Earlier, completely strongly porous sets and some of their properties were studied in the paper of V. V. Bilet and O. A. Dovgoshey [Real Anal. Exch. 39, No. 1, 175–206 (2014; Zbl 1303.28003)].

MSC:

28A10 Real- or complex-valued set functions
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets

Citations:

Zbl 1303.28003
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References:

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