ar X iv : 1 10 1 . 14 26 v 1 [ m at h . C A ] 7 J an 2 01 1 How large dimension guarantees a given angle ?

Abstract

We study the following two problems: (1) Given n ≥ 2 and α, how large Hausdorff dimension can a compact set A ⊂ R have if A does not contain three points that form an angle α? (2) Given α and δ, how large Hausdorff dimension can a compact subset A of a Euclidean space have if A does not contain three points that form an angle in the δ-neighborhood of… (More)

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