An independency result in connectification theory (Q2761032)

\textit{J. R. Porter} and \textit{R. G. Woods} [Topology Appl. 68, No. 2, 113-131 (1996; Zbl 0855.54025)] proved that any Hausdorff space with no more than \(2^{\mathfrak c}\) clopen sets can be densely embedded in a connected Hausdorff space provided it contains no nonempty proper feebly compact clopen subset. In the paper under review the authors show that validity of the converse within perfect \(T_3\) spaces with no more than \(2^{\mathfrak c}\) clopen sets is undecidable in ZFC. Further, they give a ZFC example showing that the converse does not hold within perfect Hausdorff spaces with at most two clopen sets.