The quasi-uniform character of a topological semigroup | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 23, Issue 2, 2015, Pages 224-230 PDF (464.46 K) | ||
| Document Type: Original Article | ||
| DOI: 10.1016/j.joems.2014.06.012 | ||
| Author | ||
| John Mastellos* | ||
| 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 | ||
| Topological embedding; Quasi-uniformity; Specialization order; T0 and not T1 space | ||
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