Ntantu, Ibula2017-03-102017-03-101985http://hdl.handle.net/10919/76467This paper investigates the compact-open topology on the set of C_k(X) of continuous real-valued functions defined on a Tychonoff space X. More precisely, we study the following problem: If P is a topological property, does there exist a topological property Q so that C_k(X) has P if and only if X has Q? Characterizations of many properties are obtained throughout the thesis, sometimes modulo some “mild” restrictions on the space X. The main properties involved are summarized in a diagram in the introduction.vi, 127 leavesapplication/pdfen-USIn CopyrightLD5655.V856 1985.N726Topological spacesFunction spacesMetric spacesDissertation