A remark about separation of 𝐾-analytic sets in the product spaces

Piątkiewicz, Leszek

doi:10.1090/S0002-9939-1985-0770555-8

A remark about separation of $K$-analytic sets in the product spaces
HTML articles powered by AMS MathViewer

by Leszek Piątkiewicz PDF

Proc. Amer. Math. Soc. 93 (1985), 363-366 Request permission

Abstract:

A direct proof, using only "classical" notions, of a well-known theorem about approximation of coanalytic sets in the plane with "large" sections by Borel sets is given. A generalization of this theorem for hereditarily $K$-analytic spaces is also considered.

References

Dimitri P. Bertsekas and Steven E. Shreve, Stochastic optimal control, Mathematics in Science and Engineering, vol. 139, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. The discrete time case. MR 511544
Douglas Cenzer and R. Daniel Mauldin, Inductive definability: measure and category, Adv. in Math. 38 (1980), no. 1, 55–90. MR 594994, DOI 10.1016/0001-8708(80)90057-2

Un cours sur les ensambles analytiques

Alexander S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337–384. MR 369072, DOI 10.1016/0003-4843(73)90012-0
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
Analytic sets, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. Lectures delivered at a Conference held at University College, University of London, London, July 16–29, 1978. MR 608794
C. A. Rogers and R. C. Willmott, On the uniformization of sets in topological spaces, Acta Math. 120 (1968), 1–52. MR 237733, DOI 10.1007/BF02394605
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