On certain infinite semigroups of order-increasing transformations II

Let X be an arbitrary poset. The semigroup I⁺(X) of all order-increasing partial one-one mappings of Xis shown to be an ample semigroup with some interesting properties. Moreover, a necessary and sufficient condition (on the totally ordered sets X and Y) for I⁺X) and I⁺(Y) to be isomorphic has been established.