A non-discrete space X with Cp(X) Menger at infinity

Angelo Bella; Rodrigo Hernández-Gutiérrez

doi:10.4995/agt.2019.10714

Authors

Angelo Bella University of Catania
Rodrigo Hernández-Gutiérrez Universidad Autonoma Metropolitana

DOI:

https://doi.org/10.4995/agt.2019.10714

Keywords:

Menger spaces, non-meager P-filter, pointwise convergence topology

Abstract

In a paper by Bella, Tokgös and Zdomskyy it is asked whether there exists a Tychonoff space X such that the remainder of C_p(X) in some compactification is Menger but not σ-compact. In this paper we prove that it is consistent that such space exists and in particular its existence follows from the existence of a Menger ultrafilter.

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Author Biographies

Angelo Bella, University of Catania

Department of Mathematics and Computer Science

Rodrigo Hernández-Gutiérrez, Universidad Autonoma Metropolitana

Profesor visitante

Departamento de Matematicas

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