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

Angelo Bella, Rodrigo Hernández-Gutiérrez


In a paper by Bella, Tokgös and Zdomskyy it is asked whether there exists a Tychonoff space X such that the remainder of Cp(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.


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

Subject classification

54D20; 54A35; 54C35; 54D40; 54D80; 54H11

Full Text:



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Mikołaj Krupski
Journal of the Institute of Mathematics of Jussieu  first page: 1  year: 2020  
doi: 10.1017/S1474748020000286

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