International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 311-316
A characterization of point semiuniformities
Lousiana State University at Alexandria, Division of Sciences, 8100 Highway 71 South Alexandria, 71302-9633, Louisiana, USA
Received 21 October 1994
Copyright © 1996 Jennifer P. Montgomery. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.