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Selection theorems and the reduction principle. (English) Zbl 0314.54019


MSC:

54C65 Selections in general topology
54C60 Set-valued maps in general topology
03E15 Descriptive set theory
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[1] V. Ya. Arsenin and A. A. Lyapunov, The theory of \?-sets, Uspehi Matem. Nauk (N.S.) 5 (1950), no. 5(39), 45 – 108 (Russian).
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[3] Kinjiro Kunugui, Contribution à la théorie des ensembles boreliens et analytiques, III, J. Fac. Sci. Hokkaido Imp. Univ. Ser. I. 8 (1940), 79 – 108 (French). · JFM 66.1222.01
[4] Gustave Choquet, Topology, Translated from the French by Amiel Feinstein. Pure and Applied Mathematics, Vol. XIX, Academic Press, New York-London, 1966. · Zbl 0132.17603
[5] -, Sur les théorèmes de separation dans la théorie des ensembles, Fund. Math. 26 (1936), 183-191. · JFM 62.1174.02
[6] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 397 – 403 (English, with Russian summary). · Zbl 0152.21403
[7] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143 – 178. · Zbl 0222.02075
[8] E. Michael, Selected Selection Theorems, Amer. Math. Monthly 63 (1956), no. 4, 233 – 238. · Zbl 0070.39502
[9] T. Parthasarathy, Selection theorems and their applications, Lecture Notes in Mathematics, Vol. 263, Springer-Verlag, Berlin-New York, 1972. · Zbl 0239.54011
[10] John von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401 – 485. · Zbl 0034.06102
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