open generalized shifts

Suppose x is a topological space with at least two elements, gamma$ is a nonempty set,varphi:gammato gamma is arbitrary and x^gamma$ equipped with product topology. in the following text we prove for discrete x, the generalized shift sigma_varphi:x^gammato x^gamma is an open map if and only if there exists finitesubset f of gamma$ such that varphirestriction_{gammasetminus f}:gammasetminus ftogamma$ is one--to--one. moreover for non--discrete x, the generalized shift sigma_varphi:x^gammato x^gamma is an open map if and only ifvarphi:gammato gamma is one--to--one.