Geodesic
Supplements to Michael's theorem on continuous selections, and their applications
Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 279-292 Cet article a éte moissonné depuis la source Math-Net.Ru

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Michael's well-known theorem on continuous selections is supplemented by ten equivalent conditions. The basic applications of the result obtained relate to the investigation of subdifferentiability of sublinear operators with values in spaces of continuous functions. Also, criteria are found for metrizability of convex dyadic compacta and symmetric convex Eberlein compacta, and for separability for certain classes of Banach spaces. 
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     title = {Supplements to {Michael's} theorem on continuous selections, and their applications},
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Yu. E. Linke. Supplements to Michael's theorem on continuous selections, and their applications. Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 279-292. http://geodesic.mathdoc.fr/item/SM_1994_77_2_a1/

[1] Linke Yu. E., “Ob opornykh mnozhestvakh sublineinykh operatorov”, DAN SSSR, 207:3 (1972), 531–533 | MR | Zbl

[2] Linke Yu. E., “Sublineinye operatory so znacheniyami v prostranstvakh nepreryvnykh funktsii”, DAN SSSR, 228:3 (1976), 540–542 | MR | Zbl

[3] Kusraev A. G., Kutateladze S. S., Subdifferentsialnoe ischislenie, Nauka, Novosibirsk, 1987 | MR

[4] Michael E., “A selection theorem”, Proc. Amer. Math. Soc., 17 (1966), 1404–1407 | DOI | MR

[5] Mägerl G., “Metrizability of compact sets and continuous selections”, Proc. Amer. Math. Soc., 72:3 (1978), 607–612 | DOI | MR | Zbl

[6] Weizsacker H., “Some negative results in the theory of lifting”, Lect. Notes in Math., 543, 1976, 159–172 | MR

[7] Corson H. H., Lindenstrauss I., “Continuous selections with non metrizable zone”, Trans. Amer. Math. Soc., 121:2 (1966), 492–504 | DOI | MR | Zbl

[8] Engelking E., Obschaya topologiya, Mir, M., 1986

[9] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968 | MR

[10] Corson H. H., Lindenstrauss I., “On weakly compact subsets of Banach spaces”, Proc. Amer. Math. Soc, 17, 407–412 | DOI | MR | Zbl

[11] Arkhangelskii A. V., Ponomarev V. I., Osnovy obschei topologii v zadachakh i uprazhneniyakh, Nauka, M., 1974 | MR

[12] Efimov B. A., “Diadicheskie bikompakty”, Tr. MMO, 14, URSS, M., 1965, 211–247 | MR

[13] Lindenstrauss I., “Weakly compact sets – their topological properties and the Banach spaces they generate”, Ann. Math. Stud., 1972, no. 69, 235–273 | MR | Zbl

[14] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, IL, M., 1962

[15] Lindenstrauss I., Tzafriri L., Classical Banach spaces, V. 1, Springer-Verlag, Berlin, 1977

[16] Linke Yu. E., “O suschestvovanii opornykh operatorov k sublineinym operatoram so znacheniyami v $C(Q)$”, Optimizatsiya (Novosibirsk), 1972, no. 8 (25), 52–70 | MR

[17] Hormander L., “Sur la fonction d'appui des ensembles convexes dans une espace localement convexe”, Arkiv for Math., 3:2 (1955), 181–186 | DOI | MR

[18] Kutateladze S. S., Rubinov A. M., Dvoistvennost Minkovskogo i ee prilozheniya, Nauka, Novosibirsk, 1976 | MR

[19] Gelfand I. M., “Abstraktnye funktsii i lineinye operatory”, Matem. sb., 4 (38) (1938), 235–286 | Zbl

[20] Singer I., Bases in Banach spaces, V. 2, Springer-Verlag, Berlin a.o., 1981 | MR | Zbl

[21] Plichko A. N., “Suschestvovanie totalnoi biortogonalnoi sistemy v banakhovom prostranstve”, Teoriya funktsii, funktsion. analiz i ego pril., no. 33, Kharkov, 1980, 111–118 | MR | Zbl

[22] Banach S., Thèorie des op'erations linearres, Monografje Matématyczne, Warsaw, 1932 | Zbl