Filter convergence in \(\beta\omega\)

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.

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Bibliographic Details
Published in:arXiv.org 2012-04
Main Author: Verner, Jonathan L
Format: Article
Language:English
Subjects:
Combinatorial analysis
Convergence
Online Access:Get full text
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Summary: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.
ISSN:2331-8422