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- W2460656337 abstract "Abstract In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank at most n is proper and admits an intrinsic isometric embedding into E2n+1. Since every n-dimensional Riemannian manifold is a pro-Euclidean space of rank at most n, this result is a partial generalization of (the C 0 version of) the famous Nash isometric embedding theorem from [10]." @default.
- W2460656337 created "2016-07-22" @default.
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- W2460656337 date "2015-10-29" @default.
- W2460656337 modified "2023-09-24" @default.
- W2460656337 title "Isometric Embeddings of Pro-Euclidean Spaces" @default.
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- W2460656337 doi "https://doi.org/10.1515/agms-2015-0019" @default.
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