In this paper, we redefine the concept of prime L-fuzzy ideals of an ordered semigroup so that the prime L-fuzzy ideals are not necessarily 2-valued. Then a topological space, called the spectrum of prime L-fuzzy ideals of an ordered semigroup, has been obtained and some topological properties like separation axioms, compactness, connectedness are researched. Further, a contravariant functor from the category of commutative ordered semigroups into the category of compact and connected topological spaces is gotten. Finally, we focus on the subspace which is defined in the set of all minimal prime ideals in an ordered semigroup S and show that if S is commutative, then this subspace is Hausdorff, totally disconnected and completely regular.
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