Alessandro Fedeli, Attilio Le Donne
An independency result in connectification theory

Comment.Math.Univ.Carolinae 40,2 (1999) 331-334.

Abstract:A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. \par Let $\psi $ be the following statement: ``a perfect $T_3$-space $X$ with no more than $2^{\frak c}$ clopen subsets is connectifiable if and only if no proper nonempty clopen subset of $X$ is feebly compact". \par In this note we show that neither $\psi $ nor $\neg \psi $ is provable in ZFC.

Keywords: connectifiable, perfect, feebly compact
AMS Subject Classification: 54D25, 54C25, 03E35