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Perfect compactifications of functions

Giorgio Nordo;  Boris A. Pasynkov — 2000

Commentationes Mathematicae Universitatis Carolinae

We prove that the maximal Hausdorff compactification χ f of a T 2 -compactifiable mapping f and the maximal Tychonoff compactification β f of a Tychonoff mapping f (see [P]) are perfect. This allows us to give a characterization of all perfect Hausdorff (respectively, all perfect Tychonoff) compactifications of a T 2 -compactifiable (respectively, of a Tychonoff) mapping, which is a generalization of two results of Skljarenko [S] for the Hausdorff compactifications of Tychonoff spaces.

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