On perfect bicompactifications of continuous mappings (Q2638587)

In this article the author introduces the property mentioned in the title. Some of the early sixties results of \textit{E. V. Skljarenko} are extended. A bicompact map here stands for a perfect one; a bicompactification of a mapping \(f: X\to Y\) is its bicompact extension \(bf: \tilde X\to Y\) such that \(\bar X_{\tilde X}=\tilde X\). Given regular \(T_ 1\)-spaces X and Y and an onto map \(f: X\to Y\). Five conditions are proved to be equivalent to one of a perfect bicompactification bf. Two samples are as follows: (*) For the maximal Tichonoff bicompactification \(\beta f: \beta_ fX\to Y\) of a mapping f, the natural mapping \(\phi: \beta_ fX\to \tilde X\) is monotone. (**) The growth \(\tilde X\setminus X\) does not decompose the space \(\tilde X\) at any point (the definition of a closed set that decomposes X is provided in the paper).