We investigate topological structuers on a semi-hoop A and under conditions show that there exists a topology T on A such that (A; T ) is a topological semi-hoop. We prove that for each cardinal number α there exists a topological semi-hoop of order α Finally, the separation axioms on topological semi-hoops are study and show that for any in α nite cardinal number α there exists a Hausdor ff topological semi-hoop of order α with non-trivial topology