论文标题
粗糙和Lipschitz的普遍性
Coarse and Lipschitz universality
论文作者
论文摘要
在本文中，我们提供了几种\ emph {metric通用}结果。我们展示某些类的公制空间的$ \ cc $，公制空间$（m_i，d_i）_ {i \ in i} $，其属性具有公制空间$ $（x，d_x）$ in $ \ cc $ in $ \ cc $的属性。 Lipschitzly，如果$ \ cc $中的所有空间的通用，则如果空间的集合$（m_i，d_i）_ {i \ in I} $ equi-coare coare equi-lipschitzly，则嵌入$（x，d_x）$。这些家庭的建造为某些$ \ co $的Schreier型公制子集。我们推断出对Bourgain定理的度量类似物，该定理概括了Szlenk的定理，并证明，对于所有可分开的反射渐近线 - $ C_0 $ BANACH的空间对于所有可分开的度量空间来说都是普遍的。在马丁的公理和连续假设的否定下，我们的粗糙普遍性结果之一是有效的。我们讨论没有这些额外的理论假设的普遍性声明的强度。在本文的第二部分中，我们研究了卡尔顿交织图的普遍性。特别是，我们证明，每个有限的度量空间几乎嵌入在足够大直径的一些交织图中。
In this paper we provide several \emph{metric universality} results. We exhibit for certain classes $\cC$ of metric spaces, families of metric spaces $(M_i, d_i)_{i\in I}$ which have the property that a metric space $(X,d_X)$ in $\cC$ is coarsely, resp. Lipschitzly, universal for all spaces in $\cC$ if the collection of spaces $(M_i,d_i)_{i\in I}$ equi-coarsely, respectively equi-Lipschitzly, embeds into $(X,d_X)$. Such families are built as certain Schreier-type metric subsets of $\co$. We deduce a metric analog to Bourgain's theorem, which generalized Szlenk's theorem, and prove that a space which is coarsely universal for all separable reflexive asymptotic-$c_0$ Banach spaces is coarsely universal for all separable metric spaces. One of our coarse universality results is valid under Martin's Axiom and the negation of the Continuum Hypothesis. We discuss the strength of the universality statements that can be obtained without these additional set theoretic assumptions. In the second part of the paper, we study universality properties of Kalton's interlacing graphs. In particular, we prove that every finite metric space embeds almost isometrically in some interlacing graph of large enough diameter.
