Collared and non-collared manifold boundaries

Abstract

We gather in this note results and examples about collared and non-collared boundaries in non-metrisable manifolds. It has been known for a long time that boundaries are collared in metrisable manifolds, but the matter is more complicated for non-metrisable ones. The majority of the contents of this note are well known but a bit scattered in the literature (sometimes with small inaccuracies that we correct), and some of it is apparently not published at all and might be new.