A Reuniformization for Contractive Mappings in Uniform Spaces

Abstract

Let X be a complete uniform HAUSDORFF space with a uniformity generated by a saturated family of pseudometrics 𝔄 = {ϱα(x, y): α ϵ A} and let T: X X be a continuous mapping. The paper contains necessary and sufficient conditions for the existence of a new family of pseudometrics 𝔄*={ϱ*(x, y): α*ϵA*} generated the same topology such that T is contractive with respect to 𝔄*.