Two ideals connected with strong right upper porosity at a point

TL;DR

This paper investigates the structure of certain ideals related to strongly porous sets at zero in the real numbers, revealing properties and relationships among these mathematical objects.

Contribution

It characterizes properties of sets within the intersection of maximal ideals of strongly porous sets and compares different classes of such sets.

Findings

Sets in the intersection of maximal ideals have specific characteristic properties.

The ideal generated by completely strongly porous sets is a proper subideal of the intersection.

The paper advances understanding of the algebraic structure of strongly porous sets at zero.

Abstract

Let $SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb R^{+}$ and let $\hat I(SP)$ be the intersection of maximal ideals $I \subseteq SP$. Some characteristic properties of sets $E\in\hat I(SP)$ are obtained. 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 $\hat I(SP).$