Some results connected with a problem of Erdős. III
HTML articles powered by AMS MathViewer
- by J. Arias de Reyna PDF
- Proc. Amer. Math. Soc. 89 (1983), 291-292 Request permission
Abstract:
It is shown that if $E$ is a subset with more than two points of the real line, then there exists a subset $S$ of the unit interval, such that $S$ has outer Lebesgue measure one and $S$ is of the second Baire category and such that $S$ does not contain a subset similar (in the sense of elementary geometry) to $E$. This result is related to a conjecture of P. Erdös.References
-
P. Erdös, Problems, Math. Balkanica (Papers presented at the Fifth Balkan Mathematical Congress) 4 (1974), 203-204.
- K. Kuratowski and A. Mostowski, Set theory, PWN—Polish Scientific Publishers, Warsaw; North-Holland Publishing Co., Amsterdam, 1968. Translated from the Polish by M. Maczyński. MR 0229526
- Harry I. Miller, Some results connected with a problem of Erdős. II, Proc. Amer. Math. Soc. 75 (1979), no. 2, 265–268. MR 532148, DOI 10.1090/S0002-9939-1979-0532148-4
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 291-292
- MSC: Primary 28A05; Secondary 26A21
- DOI: https://doi.org/10.1090/S0002-9939-1983-0712640-0
- MathSciNet review: 712640