The quasi-uniform character of a topological semigroup.

The topological embedding of a topological semigroup S, commutative with the property of cancelation, into the group G = S × S=/R, (R the equivalence (a; b) R(a', b;) (⇔) ab' = a'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. [ABSTRACT FROM AUTHOR]