# Article

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Keywords:
Hausdorff (Tychonoff) mapping; compactification of a mapping; maximal Hausdorff (Tychonoff) compactification of a mapping; perfect compactification of a mapping
Summary:
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.
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