On convex sets in linear normed spaces
نویسندگان
چکیده
منابع مشابه
On the Size of Approximately Convex Sets in Normed Spaces
Let X be a normed space. A set A ⊆ X is approximately convex if d(ta + (1 − t)b, A) ≤ 1 for all a, b ∈ A and t ∈ [0, 1]. We prove that every n-dimensional normed space contains approximately convex sets A with H(A,Co(A)) ≥ log2 n− 1 and diam(A) ≤ C √ n(lnn), where H denotes the Hausdorff distance. These estimates are reasonably sharp. For every D > 0, we construct worst possible approximately c...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1942
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1942-07629-4