| Title:
|
A basic approach to the perfect extensions of spaces (English) |
| Author:
|
Nordo, Giorgio |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
571-580 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
extension |
| Keyword:
|
maximal extension |
| Keyword:
|
perfect extension |
| Keyword:
|
perfect pair |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 0937.54014 |
| idMR:
|
MR1485078 |
| . |
| Date available:
|
2009-01-08T18:36:22Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118955 |
| . |
| Reference:
|
[D] Diamond B.: A characterization of those spaces having zero-dimensional remainders.Rocky Mountain Journal of Math. 15 1 (1985), 47-60. Zbl 0572.54022, MR 0779251 |
| Reference:
|
[E] Engelking R.: General Topology.Monografie Matematyczne, Warzawa, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[PW] Porter J.R., Woods R.G.: Extensions and absolutes of Hausdorff spaces.Springer, 1988. Zbl 0652.54016, MR 0918341 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| . |
