Selection theorems and invariance of Borel pointclasses

Bhattacharya, Sreela; Srivastava, S. M.

doi:10.1090/S0002-9939-1986-0845992-4

Selection theorems and invariance of Borel pointclasses
HTML articles powered by AMS MathViewer

by Sreela Bhattacharya and S. M. Srivastava PDF

Proc. Amer. Math. Soc. 97 (1986), 707-711 Request permission

Abstract:

We generalize some known selection theorems and give simple proofs of results on the invariance of Borel pointclasses obtained by Saint-Raymond, Jayne and Rogers, and Kunen and Miller.

References

Gabriel Debs, Sélection d’une multi-application à valeurs ${\cal G}_{\delta }$, Acad. Roy. Belg. Bull. Cl. Sci. (5) 65 (1979), no. 5, 211–216 (French). MR 559141
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
J. E. Jayne and C. A. Rogers, Invariance of Borel classes in metric spaces, Math. Ann. 263 (1983), no. 3, 323–341. MR 704298, DOI 10.1007/BF01457135
J. E. Jayne and C. A. Rogers, The invariance of the absolute Borel classes, Convex analysis and optimization (London, 1980) Res. Notes in Math., vol. 57, Pitman, Boston, Mass.-London, 1982, pp. 118–151. MR 647481
Kenneth Kunen and Arnold W. Miller, Borel and projective sets from the point of view of compact sets, Math. Proc. Cambridge Philos. Soc. 94 (1983), no. 3, 399–409. MR 720790, DOI 10.1017/S0305004100000785
K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
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
E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647–651. MR 109343
Jean Saint-Raymond, Fonctions boréliennes sur un quotient, Bull. Sci. Math. (2) 100 (1976), no. 2, 141–147 (French). MR 460578