A characterization of point semiuniformities (Q1912327)

Summary: The concept of a uniformity was developed by \textit{A. Weil} [Sur les espaces à structure uniforme et sur la topologie générale (1938; Zbl 0019.18604)] 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.