Innite Combinatorics and the theorems of Steinhaus and Ostrowski
نویسندگان
چکیده
We de ne combinatorial principles which unify and extend the classical results of Steinhaus and Piccard on the existence of interior points in the distance set. Thus the measure and category versions are derived from one topological theorem on interior points applied to the usual topology and the density topology on the line. Likewise we unify the subgroup theorem by reference to a Ramsey property. A combinatorial form of Ostrowskis theorem (that a bounded additive function is linear) permits the deduction of both the measure and category automatic continuity theorem for additive functions. Classi cation: 26A03; 04A15; 02K20. Keywords: In nite combinatorics, subuniversal set, Ramsey theory, No Trumps Principle, Baire property, measurability, measurecategory duality, density topology, distance set, subgroup theorem, automatic continuity.
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