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An independency result in connectification theory

Alessandro FedeliAttilio Le Donne — 1999

Commentationes Mathematicae Universitatis Carolinae

A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let ψ be the following statement: “a perfect T 3 -space X with no more than 2 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 ψ nor ¬ ψ is provable in ZFC.

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