In this paper we generalize the notion of {\it perfect compactification} of a Tychonoff space to a generic extension of any space by introducing the concept of {\it perfect pair}. This allow us to simplify the treatment in a basic way and in a more general setting. Some [S$_1$], [S$_2$], and [D]'s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.
@article{118955, author = {Giorgio Nordo}, title = {A basic approach to the perfect extensions of spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {571-580}, zbl = {0937.54014}, mrnumber = {1485078}, language = {en}, url = {http://dml.mathdoc.fr/item/118955} }
Nordo, Giorgio. A basic approach to the perfect extensions of spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 571-580. http://gdmltest.u-ga.fr/item/118955/
A characterization of those spaces having zero-dimensional remainders, Rocky Mountain Journal of Math. 15 1 (1985), 47-60. (1985) | MR 0779251 | Zbl 0572.54022
General Topology, Monografie Matematyczne, Warzawa, 1977. | MR 0500780 | Zbl 0684.54001
Extensions and absolutes of Hausdorff spaces, Springer, 1988. | MR 0918341 | Zbl 0652.54016
On perfect bicompact extensions, Dokl. Akad. Nauk SSSR 137 (1961), 39-41 Soviet Math. Dokl. 2 (1961), 238-240. (1961) | MR 0121777
Some questions in the theory of bicompactifications, Izv. Akad. Nauk. SSSR, Ser. Mat. 26 (1962), 427-452 Trans. Amer. Math. Soc. 58 (1966), 216-244. (1966) | MR 0143174