## 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