Borel measurable images of Polish spaces

Levi, Sandro; Maitra, Ashok

doi:10.1090/S0002-9939-1984-0749900-4

Borel measurable images of Polish spaces
HTML articles powered by AMS MathViewer

by Sandro Levi and Ashok Maitra

Proc. Amer. Math. Soc. 92 (1984), 98-102

DOI: https://doi.org/10.1090/S0002-9939-1984-0749900-4

PDF | Request permission

Abstract:

We determine the Borel class of the image of a Polish space under a Borel measurable function of class $\eta$ which maps open sets in the Polish space to Borel sets of additive class $\xi$ in the range, under a mild restriction on the inverse images of singleton sets. Our computation is based on a selection theorem proved in this article.

References

Careful choices: A last word on selectors

Über innere Abbildungen

23

On open images of

-sets

49

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
Sandro Levi, On the classification of functions in separable metric spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 69 (1980), no. 6, 308–312 (1982) (English, with Italian summary). MR 690296
Ashok Maitra, Selectors for Borel sets with large sections, Proc. Amer. Math. Soc. 89 (1983), no. 4, 705–708. MR 719000, DOI 10.1090/S0002-9939-1983-0719000-7
Douglas E. Miller, Borel selectors for separated quotients, Pacific J. Math. 91 (1980), no. 1, 187–198. MR 612898
S. M. Srivastava, Selection theorems for $G_{\delta }$-valued multifunctions, Trans. Amer. Math. Soc. 254 (1979), 283–293. MR 539919, DOI 10.1090/S0002-9947-1979-0539919-3
Robert Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974/75), 269–294. MR 363912, DOI 10.4064/fm-82-3-269-294