| Title:
|
Perfect compactifications of functions (English) |
| Author:
|
Nordo, Giorgio |
| Author:
|
Pasynkov, Boris A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
619-629 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the maximal Hausdorff compactification $\chi f$ of a $T_2$-compactifi\-able 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. (English) |
| Keyword:
|
Hausdorff (Tychonoff) mapping |
| Keyword:
|
compactification of a mapping |
| Keyword:
|
maximal Hausdorff (Tychonoff) compactification of a mapping |
| Keyword:
|
perfect compactification of a mapping |
| MSC:
|
54C05 |
| MSC:
|
54C10 |
| MSC:
|
54C20 |
| MSC:
|
54C25 |
| MSC:
|
54D15 |
| MSC:
|
54D30 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 1038.54010 |
| idMR:
|
MR1795091 |
| . |
| Date available:
|
2009-01-08T19:05:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119195 |
| . |
| Reference:
|
[A] Arhangel'skii A.V.: Relative topological properties and relative topological spaces.Topology Appl. 70 (1996), 87-99. Zbl 0848.54016, MR 1397067 |
| Reference:
|
[BN] Bludova I.V., Nordo G.: On the posets of all the Hausdorff and all the Tychonoff compactifications of continuous mappings.Questions & Answers Gen. Topology 17 (1999), 47-55. MR 1683951 |
| Reference:
|
[C] Chaber J.: Remarks on open-closed mappings.Fund. Math. 74 (1972), 197-208. Zbl 0242.54009, MR 0303487 |
| Reference:
|
[D] Diamond B.: A characterization of those spaces having zero-dimensional remainders.Rocky Mountain J. Math. 15 1 (1985), 47-60. Zbl 0572.54022, MR 0779251 |
| Reference:
|
[E] Engelking R.: General Topology.Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[HI] Henriksen M., Isbell J.R.: Some properties of compactifications.Duke Math. J. 25 (1958), 83-106. Zbl 0081.38604, MR 0096196 |
| Reference:
|
[M] Mazroa E.M.R.: Perfect compactifications of continuous mappings.Vestn. Mosk. Univ. Ser. I (1990), no. 1, 23-26; Moscow Univ. Math. Bull. 45 (1990), no. 1, 24-26. MR 1064275 |
| Reference:
|
[N] Nordo G.: A basic approach to the perfect extensions of spaces.Comment. Math. Univ. Carolinae 38.3 (1997), 571-580. Zbl 0937.54014, MR 1485078 |
| Reference:
|
[No] Norin V.P.: On proximities for mappings.Vestn. Mosk. Univ. Math. Mech. Ser. I 1982, no. 4 (1982), 33-36; Moscow Univ. Math. Bull. 37, no. 4 (1982), 40-44. Zbl 0508.54023, MR 0671884 |
| Reference:
|
[P] Pasynkov B.A.: On extension to mappings of certain notions and assertions concerning spaces.in: Mapping and Functors, Izdat. MGU, Moscow, 1984, pp.72-102 (in Russian). MR 0791256 |
| Reference:
|
[S] Skljarenko E.G.: On perfect bicompact extensions.Dokl. Akad. Nauk SSSR 137 (1961), 39-41; English transl.: Soviet Math. Dokl. 2 (1961), 238-240. MR 0121777 |
| Reference:
|
[W] Whyburn G.T.: Compactification of mappings.Math. Ann. 166 (1966), 168-174. Zbl 0141.20505, MR 0200905 |
| . |
