An equivalent condition for a uniform space to be coverable
General Topology
2007-10-11 v2 Algebraic Topology
Metric Geometry
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.
Cite
@article{arxiv.0707.3608,
title = {An equivalent condition for a uniform space to be coverable},
author = {Conrad Plaut},
journal= {arXiv preprint arXiv:0707.3608},
year = {2007}
}