$\sigma$-Porosity of Certain Ideals

TL;DR

This paper studies the $\sigma$-porosity property of specific ideals of subsets of natural numbers, exploring a strong form of smallness in metric spaces and identifying which ideals possess this property.

Contribution

It characterizes the $\sigma$-porosity of known ideals of subsets of natural numbers, advancing understanding of smallness notions in metric spaces.

Findings

Certain ideals are proven to be $\sigma$-porous

Identification of which known ideals are $\sigma$-porous

Clarification of the relationship between $\sigma$-porosity and meagerness

Abstract

We investigate the $\sigma$-porosity of certain known ideals of subsets of natural numbers. Porosity is a notion of smallness in metric spaces that is stronger than nowhere density. Analogously, $\sigma$-porosity is a strengthening of meagerness. In this paper, we verify which ideals are $\sigma$-porous.