The Compact-Open Topology on C(x)

This monograph offers a comprehensive study on the classical Compact-Open topology on the space $C(X)$ of all real valued continuous functions on a Tychonoff space $X$. It makes $C(X)$ a locally convex space. The space $C(X)$ equipped with the compact-open topology $k$ is denoted by $C_k(X)$. In this monograph, the authors have adopted an analytical approach, by considering $C_k(X)$ as a locally convex space. Consequently, the authors give easy and shorter proofs of several results about $C_k(X)$. The authors also provide a short historic perspective on compact-open topology.

This monograph touches almost all aspects of the compact-open topology. In particular, it includes a detailed study of the topological properties of compact-open topology on $C(X)$. A complete chapter is devoted to study compact and dense subsets of the space $C_k(X)$. Since $C_k(X)$ is a locally convex space, in Chapter 8, the authors provide a detailed study of the dual of this locally convex space. In the final chapter, the authors present several functional analytic properties of this locally convex space.

This monograph has a wide appeal to mathematicians in various fields. Chapters 2, 4 and 5 are of interest to topologists, while Chapters 8 and 9 are of interest to functional analysts. Chapters 3, 6 and 7, meanwhile, are of interest to both topologists and functional analysts.