I-Completeness in Function Spaces

Abstract

In this paper we have studied the idea of ideal completeness of function spaces Y to the power X with respect to pointwise uniformity and uniformity of uniform convergence. Further involving topological structure on X we have obtained relationships between the uniformity of uniform convergence on compacta on Y to the power X and uniformity of uniform convergence on Y to the power X in terms of I-Cauchy condition and I-convergence of a net. Also using the notion of a k-space we have given a sufficient condition for C(X,Y) to be ideal complete with respect to the uniformity of uniform convergence on compacta.