Some Properties of Semi-continuous Functions and Quasi-uniform Spaces

J. Ferrer, V. Gregori, I._L. Reilly

This paper approaches the problem of characterizing the topological spaces that admit a unique compatible quasi-uniform structure by means of semi-continuous functions. The desired result is achieved by relating properties of the semi-continuous quasi-uniformity with a new characterization of hereditarily compact spaces via lower semi-continuous functions.