# Compactness of maximal eventually different families

## TL;DR

This paper investigates the structure and existence of effectively closed and compact maximal eventually different families of functions in certain product spaces, providing criteria for their existence.

## Contribution

It introduces a characterization of when effectively compact maximal eventually different families exist in product spaces of functions.

## Key findings

- Existence criteria for effectively compact families.
- Characterization of effectively closed maximal families.
- Conditions for the existence of such families.

## Abstract

We show that there is an effectively closed maximal eventually different family of functions in spaces of the form $\prod_n F(n)$ for $F\colon \mathbb{N} \to \mathbb{N}\cup\{\mathbb{N}\}$ and give an exact criterion for when there exists an effectively compact such family.