| Title:
|
Hereditarily normal Katětov spaces and extending of usco mappings (English) |
| Author:
|
Shishkov, Ivailo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
183-196 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions. (English) |
| Keyword:
|
set-valued mapping |
| Keyword:
|
usco mapping |
| Keyword:
|
extension of maps |
| Keyword:
|
selection |
| MSC:
|
54C20 |
| MSC:
|
54C60 |
| MSC:
|
54C65 |
| MSC:
|
54D15 |
| idZBL:
|
Zbl 1037.54501 |
| idMR:
|
MR1756939 |
| . |
| Date available:
|
2009-01-08T18:59:55Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119153 |
| . |
| Reference:
|
[1] Choban M.: Set-valued mappings and Borel sets (in Russian).Trudy MMO 23 (1970), 277-301. |
| Reference:
|
[2] Choban M., Nedev S.: Factorization theorems for set-valued mappings, set-valued sections and topological dimension (in Russian).Mat. Balkanica 4 (1974), 457-460. MR 0388328 |
| Reference:
|
[3] Gutev V.: Open mappings looking like projections.Set-Valued Analysis 1 (1993), 247-260. Zbl 0818.54011, MR 1249265 |
| Reference:
|
[4] Gutev V.: Trivial bundles of spaces of probability measures and countable-dimensionality.Studia Math. 114 (1995), 1-11. Zbl 0826.46021, MR 1330213 |
| Reference:
|
[5] Gutev V.: Generic extensions of finite-valued u.s.c. selections.Topology Appl., to appear. Zbl 0998.54012, MR 1780900 |
| Reference:
|
[6] Katětov M.: On real-valued functions in topological spaces.Fund. Math. 38 (1951), 85-91. MR 0050264 |
| Reference:
|
[7] Katětov M.: Correction to ``On real-valued functions in topological spaces''.Fund. Math. 40 (1953), 203-205. Zbl 0053.12304, MR 0060211 |
| Reference:
|
[8] Katětov M.: On the extension of locally finite coverings (in Russian).Colloq. Math. 6 (1958), 145-151. MR 0103450 |
| Reference:
|
[9] Michael E.: Continuous selection I.Ann. Math. 63 (1956), 361-382. MR 0077107 |
| Reference:
|
[10] Michael E.: A theorem on semi-continuous set-valued functions.Duke Math. J. 26 (1959), 359-376. Zbl 0151.30805, MR 0109343 |
| Reference:
|
[11] Nedev S.: Selection and factorization theorems for set-valued mappings.Serdica 6 (1980), 291-317. Zbl 0492.54006, MR 0644284 |
| Reference:
|
[12] Przymusiński T.C., Wage M.: Collectionwise normality and extensions of locally finite coverings.Fund. Math. 109 (1980), 175-187. MR 0597065 |
| Reference:
|
[13] Tong H.: Some characterizations of normal and perfectly normal spaces.Duke Math. J. 19 (1952), 289-292. Zbl 0046.16203, MR 0050265 |
| Reference:
|
[14] Urysohn P.: Über die Mächtigkeit der zusammenhängenden Mengen.Math. Ann. 94 (1925), 262-295. MR 1512258 |
| . |
