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)

 
 

 

Some results connected with a problem of Erdős. III


Author: J. Arias de Reyna
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] P. Erdös, Problems, Math. Balkanica (Papers presented at the Fifth Balkan Mathematical Congress) 4 (1974), 203-204.
  • [2] K. Kuratowski and A. Mostowski, Set theory, 2nd ed., North-Holland, Amsterdam, 1976. MR 0229526 (37:5100)
  • [3] H. I. Miller, Some results connected with a problem of Erdös. II, Proc. Amer. Math. Soc. 75 (1979), 265-268. MR 532148 (82c:28003)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A05, 26A21

Retrieve articles in all journals with MSC: 28A05, 26A21


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0712640-0
Keywords: Lebesgue measure, Baire category
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society