Abstract The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient condition on an infinite metric space M, under which the transportation cost space on M contains an isometric copy of l 1 . The obtained condition is applied to answer the open questions asked by Cuth and Johanis (2017) concerning several specific metric spaces. (2) The description of the transportation cost space of a weighted finite graph G as the quotient l 1 ( E ( G ) ) / Z ( G ) , where E ( G ) is the edge set and Z ( G ) is the cycle space of G.

中文翻译：

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运输成本空间与ℓ1的关系

摘要 本文讨论了运输成本空间的一些结构性质，也称为Arens-Eells 空间、Lipschitz-free 空间和Wasserstein 空间。这项工作的主要结果是： (1) 无限度量空间 M 上的充分必要条件，在该条件下，M 上的运输成本空间包含 l 1 的等距副本。获得的条件用于回答 Cuth 和 Johanis (2017) 提出的关于几个特定度量空间的开放性问题。(2) 加权有限图 G 的运输成本空间描述为商 l 1 ( E ( G ) ) / Z ( G ) ，其中 E ( G ) 是边集， Z ( G ) 是圈G 的空间。