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Keywords:
connectifiable; perfect; feebly compact
connectifiable; perfect; feebly compact
Summary:
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.
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