Characterizations of $\mathbb{N}$-compactness and realcompactness via ultrafilters in the absence of the axiom of choice

AliReza Olfati, Eliza Wajch

This article concerns the Herrlich-Chew theorem stating that a Hausdorff zero-dimensional space is $\mathbb{N}$-compact if and only if every clopen ultrafilter with the countable i…