预切空间的一致有界性与局部强单侧空度
Uniform boundedness of pretangent spaces and local strong one-side porosity
摘要：
设（X，d，p）是点度量空间. X在p处的预切空间是由收敛于p的序列（x_n）x_PDMATHABMM X的等价类组成的度量空间，其收敛阶与给定的标度序列（r_n）r_n \downarrow 0相当.我们说（r_n）是正规的，如果存在（x_n）使得|d（x_n，p）-r_n|对于n个\to \infty，=o（r_n）。设Omega_{p} ^{X}（n）是X在p处具有正规标度序列的预切空间的集合。证明了来自Omega_{p} ^{X}（n）的空间是一致有界的当且仅当{d（x，p：x \in X}是所谓的完全强多孔集.
英文摘要：
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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