ar X iv : m at h / 02 01 07 7 v 3 [ m at h . G N ] 1 6 Ja n 20 03 A family of pseudo metrics on B 3 and its application
نویسندگان
چکیده
We define a family of pseudo metrics on B and study elementary properties of the associated metric spaces. As an application we prove that, for any a > 0 and for any countable-to-one function f from (S, dE) to [0, a], the set NMnf = {x ∈ S 2 | ∃y ∈ S such that f(x)− f(y) > ndE(x, y)} is uncountable for all n ∈ N, where dE is the standard Euclidean metric on S = { (x, y, z) ∈ R | x + y + z = 1 }
منابع مشابه
ar X iv : m at h / 02 01 07 7 v 5 [ m at h . G N ] 1 5 Fe b 20 07 A family of pseudo metrics on B 3 and its application
Let B be the closed unit ball in R and S its boundary. We define a family of pseudo metrics on B. As an application, we prove that for any countable-to-one function f : S → [0, a], the set NMnf = {x ∈ S 2 | there exists y ∈ S2 such that f(x)−f(y) > ndE(x, y)} is uncountable for all n ∈ N, where dE is the Euclidean metric on R . 2000 Mathematics Subject Classification ; 57N05, 57M40 1 The family...
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