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arXiv · 1604.02049

Unions and ideals of locally strongly porous sets

Maya Altinok·Oleksiy Dovgoshey·Mehmet Küçükaslan
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Abstract

For subsets of $\mathbb R^+ = [0,\infty)$ we introduce a notion of coherently porous sets as the sets for which the upper limit in the definition of porosity at a point is attained along the same sequence. We prove that the union of two strongly porous at $0$ sets is strongly porous if and only if these sets are coherently porous. This result leads to a characteristic property of the intersection of all maximal ideals containing in the family of strongly porous at $0$ subsets of $\mathbb R^+$. It is also shown that the union of a set $A \subseteq \mathbb R^+$ with arbitrary strongly porous at $0$ subset of $\mathbb R^+$ is porous at $0$ if and only if $A$ is lower porous at $0$.

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Maya Altinok, Oleksiy Dovgoshey, Mehmet Küçükaslan. 2017-03-24. Unions and ideals of locally strongly porous sets. https://arxiv.org/abs/1604.02049

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