Quasi-Uniform Spaces I: Pervin Quasi-Uniformities, Pervin Spaces

A uniform space is a natural generalization of the notion of a metric space, on which completeness still makes sense. It is rather puzzling that I managed to avoid the subject of quasi-uniform spaces in something like the 7 years that this blog existed… and it is time that I started. I will only say very classical things, and I will concentrate one a construction due to William Pervin, simplifying an earlier result of Császár, and which shows that every topological space is quasi-uniformizable. Read the full post.