On the covering and the additivity number of the real line

Author:
Kyriakos Keremedis

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

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the real line *R* cannot be covered by *k* many nowhere dense sets iff *whenever* *is a family of dense open sets of R there exists a countable dense set G of R such that* *for all* . We also show that the union of *k* meagre sets of the real line is a meagre set iff *for every family* *of dense open sets of R and for every countable dense set G of R there exists a dense set* *such that* *for all* .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1234629-6

Keywords:
Covering number,
additivity number,
nowhere dense,
meagre,
bounding number,
dominating number

Article copyright:
© Copyright 1995
American Mathematical Society