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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 2, Pages 311-316

A characterization of point semiuniformities

Lousiana State University at Alexandria, Division of Sciences, 8100 Highway 71 South Alexandria, Louisiana 71302-9633, USA

Received 21 October 1994

Copyright © 1996 Hindawi Publishing Corporation. 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.