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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: 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 $ \vert G\backslash {D_i}\vert < \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 $ \vert Q\backslash {D_{i}}\vert < \omega $ for all $ i \in k$.


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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

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