Abstract:We prove that the maximal Hausdorff compactification $\chi f$ of a $T_2$-compactifiable 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.
Keywords: Hausdorff (Tychonoff) mapping, compactification of a mapping, maximal Hausdorff (Tychonoff) compactification of a mapping, perfect compactification of a mapping
AMS Subject Classification: Primary 54C05, 54C10, 54C20, 54C25; Secondary 54D15, 54D30, 54D35