On the minimal cardinality of a subset of R which is not of first category

Apoloniusz Tyszka

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On the minimal cardinality of a subset of R which is not of first category

Apoloniusz Tyszka

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Abstract

Let M be the ideal of first category subsets of R and non(M)=min{card X: X \subseteq R, X \not\in M}. We consider families Φof sequences converging to \infty, with the property that for every open set U \subseteq R that is unbounded above there exists a sequence belonging to Φ, which has an infinite number of terms belonging to U. We present assumptions about Φwhich imply that the minimal cardinality of Φequals non(M).

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BibTeX RIS

Apoloniusz Tyszka. 1999-09-27. On the minimal cardinality of a subset of R which is not of first category. https://arxiv.org/abs/math/9907090

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