International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 311-316
doi:10.1155/S0161171296000439

A characterization of point semiuniformities

Abstract

The concept of a uniformity was developed by A. Well and there have been several generalizations. This paper defines a point semiuniformity and gives necessary and sufficient conditions for a topological space to be point semiuniformizable. In addition, just as uniformities are associated with topological groups, a point semiuniformity is naturally associated with a semicontinuous group. This paper shows that a point semiuniformity associated with a semicontinuous group is a uniformity if and only if the group is a topological group.