On loop functions in the theory of topological LA-semigroups

In theory of topological LA-semigroups, we introduce the concepts of LA-loop functions for LA-lifting functions in theory of LA-fibrations. We prove that the LA-lifting function and LA-loop function for any LA-fibration are not necessarily unique. We also restrict the LA-loop function on any idempotent point in any LA-fiber space to get another LA-map which is called a LA-loop restriction.