Geodesic
Perfect compactifications of functions
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 619-629.

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We prove that the maximal Hausdorff compactification $\chi f$ of a $T_2$-compactifi\-able mapping $f$ and the maximal Tychonoff compactification $\beta f$ 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.
Classification : 54C05, 54C10, 54C20, 54C25, 54D15, 54D30, 54D35
Keywords: Hausdorff (Tychonoff) mapping; compactification of a mapping; maximal Hausdorff (Tychonoff) compactification of a mapping; perfect compactification of a mapping 
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     title = {Perfect compactifications of functions},
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Nordo, Giorgio; Pasynkov, Boris A. Perfect compactifications of functions. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 619-629. http://geodesic.mathdoc.fr/item/CMUC_2000__41_3_a17/