Filter convergence in $\beta\omega$

TL;DR

This paper establishes a combinatorial criterion for filters to support injective F-convergent sequences in βω and proves that analytic filters cannot, answering a question in topology and filter theory.

Contribution

It provides a necessary condition for filters to admit injective F-convergent sequences in βω and shows that no analytic filter satisfies this, advancing understanding of filter convergence.

Findings

A necessary combinatorial condition for filters to admit injective F-convergent sequences.

No analytic filter admits an injective F-convergent sequence in βω.

Answers an open question by Banakh, Mychaylyuk, and Zdomskyy.

Abstract

We give a necessary combinatorial condition on a filter F to admit an injective F-convergent sequence in $\beta\omega$. We also show that no analytic filter F admits an injective F-convergent sequence in $\beta\omega$. This answers a question of T. Banakh, V. Mychaylyuk and L. Zdomskyy.