ABSTRACT:It is known that free ultrafilters cannot be constructed effectively (i.e., in ZF set theory without any additional choice principle). In this paper a nonconvergent, thus free, z‐ultrafilter is constructed effectively in a suitable zero‐dimensional topological space X. Thus the implication C‐compact ?B‐compact(which under AC is an equivalence for completely regular spaces) fails to be an equivalence in ZF even for zero‐dimensional spaces, where B‐compact (respectively, C‐compact) means that every ultrafilter (respectively, z‐ultrafilter) converges.