Properties of function space under Cauchy convergence topology

Abstract

In 2020, Peng and Sun modified the definition of the Cauchy convergence topology, defined on the space of continuous functions from a metric space X to the real line R that is denoted by Cch(d)(X). In continuation of this study we examine some of the important properties of this space. First, we prove that the space Cch(d)(X) is not dense in RX. Further we find the necessary and sufficient condition for the openness of the restriction map on the space Cch(d)(X). Apart from these we find the condition for the space Cch(d)(X) to be Frechet-Uryshon space.