This is a preview of subscription content, log in via an institution to check access.
Literature Cited
E. Michael, “Continuous selections. I,” Ann. of Math.,63, No. 2, 361–382 (1956).
E. Michael, “Continuous selection. II,” Ann. of Math.,64, No. 3, 562–580 (1956).
E. Michael, “A survey of continuous selections,” in: Lecture Notes in Mathematics, No. 171, Springer-Verlag (1970), pp. 54–58.
M. M. Choban, “Multivalued mappings and Borel sets,” Dokl. Akad. Nauk SSSR,182, No. 3, 514–517 (1968).
M. M. Choban, “Multivalued mappings and certain related problems,” Dokl. Akad. Nauk SSSR,190, No. 2, 293–296 (1970).
V. A. Geiler, “On continuous selections in uniform spaces,” Dokl. Akad. Nauk SSSR,195, No. 1, 17–19 (1970).
Yu. É. Linke, “Sublinear operators and continuous selections,” in: Optimization [in Russian], Vol. 8(25), Izd. Inst. Matem. Sibrisk. Otd. Akad. Nauk SSSR, Novosibirsk (1972), pp. 71–76.
A. F. Filippov, “Classical solutions of differential equations with a multivalued right-hand side,” Vestnik Moskov. Univ. Ser. Matem. Mekh., No. 3, 16–26 (1967).
J. L. Massera and J. J. Schäffer, Linear Differential Equations and Function Spaces, Academic Press, New York (1966).
Yu. É. Linke, “The existence of supporting linear operators for sublinear operators with values in C(Q),” in: Optimization [in Russian], Vol. 8(25), Izd. Inst. Matem. Sibrisk. Otd. Akad. Nauk SSSR, Novosibirsk (1972), pp. 52–70.
S. S. Kutateladze, “A remark on the connection between selections and generators,” in: Optimization [in Russian], Vol. 8(25), Izd. Inst. Matem. Sibrisk. Otd. Akad. Nauk SSSR, Novosibirsk (1972), pp. 42–47.
Arrigo Cellina, “Approximation of set-valued functions and fixed-point theorems,” Ann. Math. Pura Appl.,82, 17–24 (1969).
B. N. Pshenichnyi, “Multivalued mappings in the theory of differential games,” in: Controllable Random Processes and Systems [in Russian], Kiev (1972), pp. 54–73.
T. Parthasarathy, “Selection theorems and their applications,” in: Lecture Notes in Mathematics, No. 263, Springer-Verlag, Berlin (1972), pp. 1–101.
N. Bourbaki, Topological Vector Spaces [Russian translation], IL, Moscow (1959).
M. M. Day, Normed Linear Spaces, Springer-Verlag, Berlin (1962).
H. H. Schaeffer, Topological Vector Spaces, Macmillan, New York (1966).
J. Cea, Optimization. Theory and Algorithms [Russian translation], Mir, Moscow (1973).
J. Ekeland, “Parametrisation en theorie de la commande,” Compt. Rend. Acad. Sci. Paris,267, No. 2, A98–xA100 (1968).
J. Ekeland and M. Valadier, “Representation of set-valued mappings,” J. Math. Analysis and Applic.,35, No. 3, 621–629 (1971).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 4, pp. 837–852, July–August, 1975.
Rights and permissions
About this article
Cite this article
Tolstonogov, A.A. The topological structure of continuous multivalued mappings. Sib Math J 16, 642–654 (1975). https://doi.org/10.1007/BF00967139
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00967139