A unified approach to measurable and continuous selections

Mägerl, G.

doi:10.1090/S0002-9947-1978-0511422-5

A unified approach to measurable and continuous selections
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Trans. Amer. Math. Soc. 245 (1978), 443-452 Request permission

Abstract:

An abstract selection theorem is presented which contains as special cases-among others-the measurable selection theorem of Kuratowski and Ryll-Nardzewski, as well as the continuous selection theorem of Michael.

References

Heinz Bauer and H. S. Bear, The part metric in convex sets, Pacific J. Math. 30 (1969), 15–33. MR 275101, DOI 10.2140/pjm.1969.30.15
H. H. Corson and J. Lindenstrauss, Continuous selections with nonmetrizable range, Trans. Amer. Math. Soc. 121 (1966), 492–504. MR 187214, DOI 10.1090/S0002-9947-1966-0187214-8
James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606

Mengenlehre

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). MR 188994

Zu den Schnittsätzen von Michael und Kuratowski & Ryll-Nardzewski

Ernest Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361–382. MR 77107, DOI 10.2307/1969615
E. Michael, Selected Selection Theorems, Amer. Math. Monthly 63 (1956), no. 4, 233–238. MR 1529282, DOI 10.2307/2310346
E. Michael, A selection theorem, Proc. Amer. Math. Soc. 17 (1966), 1404–1406. MR 203702, DOI 10.1090/S0002-9939-1966-0203702-5
A. R. Pears, Dimension theory of general spaces, Cambridge University Press, Cambridge, England-New York-Melbourne, 1975. MR 0394604
Heinrich von Weizsäcker, Some negative results in the theory of lifting, Measure theory (Proc. Conf., Oberwolfach, 1975) Lecture Notes in Math., Vol. 541, Springer, Berlin, 1976, pp. 159–172. MR 0450972