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

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

1999-07-14

arxiv.org/abs/math/9907090v7

Journal of Natural Geometry 17 (2000), pp.21-28

Mathematics

Logic

7 pages, added text about conditions C_m, to appear in J. Nat. Geom

Scientific paper

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 \Phi of 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 \Phi, which has an infinite number of terms belonging to U. We present assumptions about \Phi which imply that the minimal cardinality of \Phi equals non(M).

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