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arXiv · 1302.4599

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

Viktoriia Bilet·Oleksiy Dovgoshey
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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 (x_n), x_n \in X, whose degree of convergence is comparable with a given scaling sequence (r_n), r_n\downarrow 0. We say that (r_n) is normal if there is (x_n) such that |d(x_n,p)-r_n|=o(r_n) for n\to\infty. Let Omega_{p}^{X}(n) be the set of pretangent spaces to X at p with normal scaling sequences. We prove that the spaces from Omega_{p}^{X}(n) are uniformly bounded if and only if {d(x,p:x\in X}is a so-called completely strongly porous set.

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Viktoriia Bilet, Oleksiy Dovgoshey. 2013-02-19. Uniform boundedness of pretangent spaces and local strong one-side porosity. https://arxiv.org/abs/1302.4599

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