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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the covering and the additivity number of the real line
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by Kyriakos Keremedis PDF
Proc. Amer. Math. Soc. 123 (1995), 1583-1590 Request permission

Abstract:

We show that the real line R cannot be covered by k many nowhere dense sets iff whenever $D = \{ {D_i}:i \in k\}$ is a family of dense open sets of R there exists a countable dense set G of R such that $|G\backslash {D_i}| < \omega$ for all $i \in k$. We also show that the union of k meagre sets of the real line is a meagre set iff for every family $D = \{ {D_i}:i \in k\}$ of dense open sets of R and for every countable dense set G of R there exists a dense set $Q \subseteq G$ such that $|Q\backslash {D_{i}}| < \omega$ for all $i \in k$.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1583-1590
  • MSC: Primary 03E35; Secondary 03E05, 03E40
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1234629-6
  • MathSciNet review: 1234629