Geodesic
An independency result in connectification theory
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 331-334.

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A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. 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". In this note we show that neither $\psi$ nor $\neg \psi$ is provable in ZFC.
Classification : 03E35, 54A35, 54C25, 54D05, 54D25
Keywords: connectifiable; perfect; feebly compact 
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Fedeli, Alessandro; Le Donne, Attilio. An independency result in connectification theory. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 331-334. http://geodesic.mathdoc.fr/item/CMUC_1999__40_2_a14/