  We define the notion of the partial order of ends of the Cayley graph of a
semigroup. We prove that the structure of the ends of a semigroup is invariant
under change of finite generating set and at the same time is inherited by
subsemigroups and extensions of finite Rees index. We prove an analogue of
Hopf's Theorem, stating that a group has 1, 2 or infinitely many ends, for left
cancellative semigroups and that the cardinality of the set of ends is
invariant in subsemigroups and extension of finite Green index in left
cancellative semigroups.
