Topological Properties of C(X, Y)
Chris Alan Schwendiman · Digital Commons - USU (Utah State University) · 2021
The purpose of this paper is to examine the important topological properties of the function spaces BC(X,Y) and C(X,Y). Emphasis is given to the relationship between the metrizability of X and the separability of these function spaces. The paper is divided into three major parts: the preliminary definitions and theorems; the relationship between the topological properties of X and BC (X ,Y), for compact X; and the extension of the results of Part II for X not compact and for the case when we have C(X, Y).