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math.LO1999
A new combinatorial characterization of the minimal cardinality of a subset of R which is not of first category
Apoloniusz Tyszka
Let M denote the ideal of first category subsets of R. We prove that min{card X: X \subseteq R, X \not\in M} is the smallest cardinality of a family S \subseteq {0,1}^ωwith the pro…
math.MG1999
A discrete form of the Beckman-Quarles theorem for rational eight-space
Apoloniusz Tyszka
Let Q denote the field of rational numbers. Let F \subseteq R is a euclidean field. We prove that: (1) if x,y \in F^n (n>1) and |x-y| is constructible by means of ruler and compass…