Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Borel measurable images of Polish spaces


Authors: Sandro Levi and Ashok Maitra
Journal: Proc. Amer. Math. Soc. 92 (1984), 98-102
MSC: Primary 54H05; Secondary 28A20, 54C65
DOI: https://doi.org/10.1090/S0002-9939-1984-0749900-4
MathSciNet review: 749900
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] J. P. Burgess, Careful choices: A last word on selectors, preprint, 1979.
  • [2] F. Hausdorff, Über innere Abbildungen, Fund. Math. 23 (1934), 279-291.
  • [3] L. Keldysh, On open images of $ A$-sets, Dokl. Akad. Nauk SSSR 49 (1945), 646.
  • [4] K. Kuratowski, Topology, Vol. 1, 5th ed., Academic Press, New York, 1966. MR 0217751 (36:840)
  • [5] S. Levi, On the Baire property in separable metric spaces, Atti Accad. Naz. Lincei 69 (1980), 303-307. MR 690295 (84k:54016b)
  • [6] A. Maitra, Selectors for Borel sets with large sections, Proc. Amer. Math. Soc. 89 (1983), 705-708. MR 719000 (84k:54015)
  • [7] D. E. Miller, Borel selectors for separated quotients, Pacific J. Math. 91 (1980), 187-198. MR 612898 (82d:54016)
  • [8] S. M. Srivastava, Selection theorems for $ {G_\delta }$-valued multifunctions, Trans. Amer. Math. Soc. 254 (1979), 283-293. MR 539919 (80g:54027)
  • [9] R. L. Vaught, Invariant sets in logic and topology, Fund. Math. 82 (1974), 269-294. MR 0363912 (51:167)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H05, 28A20, 54C65

Retrieve articles in all journals with MSC: 54H05, 28A20, 54C65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0749900-4
Keywords: Polish space, Borel class of sets and functions, selectors
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society