An equivalent condition for a uniform space to be coverable

2007/07/24 by Conrad Plaut, Plaut, Conrad
Mathematics · #54E15 #55M10 (Secondary) #55Q52 (Primary) #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #Metric Geometry (math.MG) #math.AT #math.GN #math.MG #msc:54E15 #msc:55M10 #msc:55Q52

paper · pdf · doi:10.48550/arxiv.0707.3608

arxiv created 2007/10/11 · arxiv updated 2009/12/01

Abstract

We prove that an equivalent condition for a uniform space to be coverable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to find covering entourage, (2) correct an error in [3] and (3) show that coverable is equivalent to chain connected and uniformly joinable in the sense of arXiv:0706.3937.

Citations

• Rips complexes and covers in the uniform category

Related

• Illustrating an error in "An equivalent condition for a uniform space to be coverable"
• Coverings and fundamental groups: a new approach
• Generalized Universal Covers of Uniform Spaces
• Universal covering spaces, a footnote
• Every Continuum has a Compact Universal Cover