Some local subsemihypergroups of the partial transformation semigroup on a set

Abstract

In this paper, we give definitions of a local subset and a local subsemihypergroup of a semihypergroup. Moreover, we define a hyperopera- tion o on the partial transformation semigroup P(X) so that (P(X), o) is a semihypergroup. Our aim is to characterize in form of an idempotent α of the semigroup P(X) when the local subset α oG(X)o α of (P(X), o) become a local subsemihypergroup of P(X). © 2013 Academic Publications, Ltd.