Homogeneous ideals on countable sets

TL;DR

This paper explores the properties of homogeneous ideals on countable sets, providing examples, applications to topology and ideal convergence, and addressing related questions.

Contribution

It introduces the concept of homogeneous ideals, investigates their properties, and demonstrates their relevance through examples and applications.

Findings

Examples of homogeneous ideals are provided.

Applications to topology and ideal convergence are discussed.

Questions related to homogeneous ideals are answered.

Abstract

We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of homogeneous ideals and present some applications to topology and ideal convergence. Moreover, we answer questions related to our research.