Infinite-dimensional uniform polyhedra
Geometric Topology
2022-11-21 v4 Combinatorics
General Topology
Metric Geometry
Abstract
Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a cofinal family) in many separable metric spaces of interest. To get hold on uniform homotopy properties of these spaces, a reasonably behaved notion of an infinite-dimensional metric polyhedron is needed; a specific list of desired properties was sketched by J. R. Isbell in a series of publications in 1959-64. In this paper we construct what appears to be the desired theory of uniform polyhedra; incidentally, considerable information about their metric and Lipschitz properties is obtained.
Cite
@article{arxiv.1109.0346,
title = {Infinite-dimensional uniform polyhedra},
author = {Sergey A. Melikhov},
journal= {arXiv preprint arXiv:1109.0346},
year = {2022}
}
Comments
47 pages. v4: Section 4 is added