The quasi-uniform character of a topological semigroup

Document Type : Original Article

Author

Department of Mathematics, University of Patras, 26504 Patras, Greece

Abstract

The topological embedding of a topological semigroup S, commutative with the property
of cancelation, into the group G ¼ S  S=R, (R the equivalence ða; bÞRða0
; b0
Þ () ab0 ¼ a0
b) to
which S is algebraically embedded, was the subject of the search for the mathematicians of a long
period. It was based on the fact that S must naturally be a uniform topological space, as every topological group was. The present paper is devoted to the fact that a quasi-uniformity is defined to any
topological space, thus to any topological semigroup.

Keywords