# Ideals on countable sets: a survey with questions

## TL;DR

This survey reviews the theory of ideals on countable sets, highlighting key results and open questions in topology and set theory related to these structures.

## Contribution

It compiles and discusses existing results on ideals on countable sets and presents numerous open questions for future research.

## Key findings

- Summarizes foundational results on ideals on countable sets.
- Identifies key open problems in the area.
- Connects ideals to applications in topology and set theory.

## Abstract

An ideal on a set $X$ is a collection of subsets of $X$ closed under the operations of taking finite unions and subsets of its elements. Ideals are a very useful notion in topology and set theory and have been studied for a long time. We present a survey of results about ideals on countable sets and include many open questions.