On the product of primal spaces

Abstract

Let X be a set and f : X → X be a map. We denote by ????(f) the topology defined on X whose closed sets are the subsets A of X with f (A) ⊆ A. A topology on X is said to be a primal topology, if it is a ????(f) for some map f. Our aim here is to characterize when the product of an arbitrary family of topological spaces is a primal space.