Stratifications on the Ran space

Abstract

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 \v Cech simplicial complex. We show that paths in this product space respecting its stratification induce simplicial maps between the endpoints of the path.

arXiv commentFinal version, to be published in Order. Comments welcome