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.

Subiman Kundu is a Former Professor of the Department of Mathematics, Indian Institute of Technology Delhi, India.

Varun Jindal is an Assistant Professor at the Department of Mathematics, Malaviya National Institute of Technology in Jaipur, India.