We describe a partial order on finite simplicial complexes. This partial order provides a poset stratification of the product of the Ran space of a metric space and the nonnegative real numbers, through the Čech simplicial complex. We show that paths in this product space respecting its stratification induce simplicial maps between the endpoints of the path.

中文翻译：

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Ran空间的分层

我们描述了有限单纯复形的偏序。该偏序通过 Čech 单纯复形提供了度量空间的 Ran 空间与非负实数的乘积的偏序分层。我们表明，该乘积空间中的路径在考虑其分层时会在路径的端点之间产生单纯映射。