Filter convergence in $\beta\omega$

Abstract

We give a combinatorial condition which is necessary for a filter $\F$ to admit injective $\F$-convergent sequences 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.

Keywords

• analytic F -filter
• meager filter
• filter convergence
• Rudin-Keisler ordering