Connectedness of the fine topology

Abstract

This paper studies the connectedness of the fine topology on C(X, Y ), the set of all continuous functions from a Tychonoff space X to a metric space (Y, d). Occasionally, we assume Y to be a normed linear space. We also determine the components of the space H(Rn), of all self homeomorphisms on the n-dimensional Euclidean space Rn, where H(Rn) is considered as a subspace of the space C(Rn, Rn) equipped with the fine topology. © 2019 Topology Proceedings.