Hereditarily normal Katětov spaces and extending of usco mappings
Shishkov, Ivailo
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 183-196 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2000-01-01
Classification:  54C20,  54C60,  54C65,  54D15
@article{119153,
     author = {Ivailo Shishkov},
     title = {Hereditarily normal Kat\v etov spaces and extending of usco mappings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {183-196},
     zbl = {1037.54501},
     mrnumber = {1756939},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119153}
}
Shishkov, Ivailo. Hereditarily normal Katětov spaces and extending of usco mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 183-196. http://gdmltest.u-ga.fr/item/119153/

Choban M. Set-valued mappings and Borel sets (in Russian), Trudy MMO 23 (1970), 277-301. (1970)

Choban M.; Nedev S. Factorization theorems for set-valued mappings, set-valued sections and topological dimension (in Russian), Mat. Balkanica 4 (1974), 457-460. (1974) | MR 0388328

Gutev V. Open mappings looking like projections, Set-Valued Analysis 1 (1993), 247-260. (1993) | MR 1249265 | Zbl 0818.54011

Gutev V. Trivial bundles of spaces of probability measures and countable-dimensionality, Studia Math. 114 (1995), 1-11. (1995) | MR 1330213 | Zbl 0826.46021

Gutev V. Generic extensions of finite-valued u.s.c. selections, Topology Appl., to appear. | MR 1780900 | Zbl 0998.54012

Katětov M. On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85-91. (1951) | MR 0050264

Katětov M. Correction to ``On real-valued functions in topological spaces'', Fund. Math. 40 (1953), 203-205. (1953) | MR 0060211 | Zbl 0053.12304

Katětov M. On the extension of locally finite coverings (in Russian), Colloq. Math. 6 (1958), 145-151. (1958) | MR 0103450

Michael E. Continuous selection I, Ann. Math. 63 (1956), 361-382. (1956) | MR 0077107

Michael E. A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 359-376. (1959) | MR 0109343 | Zbl 0151.30805

Nedev S. Selection and factorization theorems for set-valued mappings, Serdica 6 (1980), 291-317. (1980) | MR 0644284 | Zbl 0492.54006

Przymusiński T.C.; Wage M. Collectionwise normality and extensions of locally finite coverings, Fund. Math. 109 (1980), 175-187. (1980) | MR 0597065

Tong H. Some characterizations of normal and perfectly normal spaces, Duke Math. J. 19 (1952), 289-292. (1952) | MR 0050265 | Zbl 0046.16203

Urysohn P. Über die Mächtigkeit der zusammenhängenden Mengen, Math. Ann. 94 (1925), 262-295. (1925) | MR 1512258