Uniform boundedness of pretangent spaces and local strong one-side porosity

الأصل · EN

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.