On certain infinite semi groups of order-increasing transformations II

الملخص EN

Let X be an arbitrary poset.

The semigroup I+(X) of all order-increasing partial one– one mappings of X is 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.