A remark on analytic sets with $\sigma$-compact sections
HTML articles powered by AMS MathViewer
- by V. V. Srivatsa PDF
- Proc. Amer. Math. Soc. 81 (1981), 306-307 Request permission
Abstract:
We show that there exists an analytic set $A \subset {\omega ^\omega } \times {\omega ^\omega }$ and having $\sigma$-compact vertical sections such that $A$ contains no analytic set $B$ with compact vertical sections and having the same projection to the first coordinate as $A$. This answers a question of J. R. Steel.References
- D. Blackwell and C. Ryll-Nardzewski, Non-existence of everywhere proper conditional distributions, Ann. Math. Statist. 34 (1963), 223–225. MR 148097, DOI 10.1214/aoms/1177704259
- Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
- H. Sarbadhikari, Some uniformization results, Fund. Math. 97 (1977), no. 3, 209–214. MR 494012, DOI 10.4064/fm-97-3-209-214
- 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
- John R. Steel, A note on analytic sets, Proc. Amer. Math. Soc. 80 (1980), no. 4, 655–657. MR 587948, DOI 10.1090/S0002-9939-1980-0587948-X
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 306-307
- MSC: Primary 04A15; Secondary 03E15, 28A05, 54H05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593477-0
- MathSciNet review: 593477