Universal covering spaces, a footnote

Abstract

We give a short proof that, for nice $X$, the based fundamental groupoid of $X$ with topology induced by the compact open topology on the space of paths, is indeed the universal covering space of $X$.

Short direct proof of a known (but not well-known) result about the construction of universal covering spaces. Stefan Friedl kindly pointed out to us that there was a gap in the previous version of the note. The ensuing discussion resulted in an even shorter and more straightforward proof of the theorem. We are grateful to Stefan for his helpful intervention