Polymorphisms of arity omega have recently been used in the proof of model theory results that have applications in the field of complexity of CSP problems. At the same time, the introduction of clone algebras has revitalised the algebraic study of clones of functions, and in particular of functions of arity omega. In this paper, we delve into the algebraic and topological study of polymorphisms of arity omega and of the corresponding invariant relations. % of arity omega.