Retractions in semigroups
Alexander Doniphan Wallace · Pacific Journal of Mathematics · 1957
Let S be a semigroup (that is, a Hausdorff space together with a continuous associative multiplication) and let E denote the set of idempotents of S. If xeS let, M e = {x\ex e H and xee H} , Z c =H e x{R c f\E)x{L e f\E)and Under the assumption that S is compact we shall prove that K e is a retract of M e and that K e and Z e are equivalent, both algebraically and topologically.This latter fact sharpens a result announced in [6] and the former settles several questions raised in [7].I am grateful to A. H. Clifford and to R. J. Koch for their several