Abstract

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.

Keywords: Semi-continuous function, quasi-uniform space, hereditarily compact space.

MSC: 54E35, 54E55

Pages:  11$-$18     

Volume  47 ,  Issue  1$-$2 ,  1995