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

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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