Corrections to "Lectures on Coarse Geometry"

Corrections to "Lectures on Coarse Geometry"

Bernd Grave pointed out a couple of errors in Lectures on Coarse Geometry, explained here.

One is a foolish mistake I made with Urysohn's lemma. Given two disjoint closed subsets of a compact Hausdorff space, Urysohn's lemma allows one to find a continuous function equal to zero on one set, one on the other. But in general the set of points where said function is zero will be *larger* than the originally given closed set. Only in metric spaces can one expect to arrange equality.