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Keywords:
extension; maximal extension; perfect extension; perfect pair
extension; maximal extension; perfect extension; perfect pair
Summary:
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.
References:
[D] Diamond B.: A characterization of those spaces having zero-dimensional remainders. Rocky Mountain Journal of Math. 15 1 (1985), 47-60. MR 0779251 | Zbl 0572.54022
[E] Engelking R.: General Topology. Monografie Matematyczne, Warzawa, 1977. MR 0500780 | Zbl 0684.54001
[PW] Porter J.R., Woods R.G.: Extensions and absolutes of Hausdorff spaces. Springer, 1988. MR 0918341 | Zbl 0652.54016
[S$_1$] Skljarenko E.G.: On perfect bicompact extensions. Dokl. Akad. Nauk SSSR 137 (1961), 39-41 Soviet Math. Dokl. 2 (1961), 238-240. MR 0121777
[S$_2$] Skljarenko E.G.: 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. MR 0143174
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