For a Tychonoff space \(X\), we denote by \(C_(X)\) the space of all real-valued continuous functions on \(X\) with set-open topology.
We investigate the topological-algebraic properties of \(C_(X)\) such as submetrizability, metrizability, separability and other. We also compare this topology with several well-known and lesser known topologies (for example, topology of uniform convergence).