2011/09/02 by Melikhov, Sergey A.
#Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1109.0346
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.