Let be a metric space, and a continuous surjection. An element of is a wandering point if there is a neighborhood of and an integer such that, for all , . If is not wandering, we call it a nonwandering point. Equivalently, is a nonwandering point if for every neighborhood of there is such that is nonempty. The set of all nonwandering points is called the nonwandering set of , and is denoted by .

If is compact, then is compact, nonempty, and forward invariant; if, additionally, is an homeomorphism, then is invariant.