Uniform boundedness of pretangent spaces and local strong one-side porosity
Abstract
Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (xn), xn ∈ X, whose degree of convergence is comparable with a given scaling sequence (rn), rn 0. We say that (rn) is normal if there is (xn) such that |d(xn,p)-rn|=o(rn) for n∞. Let OmegapX(n) be the set of pretangent spaces to X at p with normal scaling sequences. We prove that the spaces from OmegapX(n) are uniformly bounded if and only if d(x,p:x∈ Xis a so-called completely strongly porous set.
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