A unified approach to measurable and continuous selections
HTML articles powered by AMS MathViewer
- by G. Mägerl PDF
- 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 F. Hausdorff, Mengenlehre, de Gruyter, Berlin and Leipzig, 1927.
- 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 G. Mägerl, Zu den Schnittsätzen von Michael und Kuratowski & Ryll-Nardzewski, Dissertation, Erlangen, 1977.
- 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
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 245 (1978), 443-452
- MSC: Primary 28B20; Secondary 28A05, 54C65
- DOI: https://doi.org/10.1090/S0002-9947-1978-0511422-5
- MathSciNet review: 511422