Browsing by Author "Ntantu, Ibula"
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- The compact-open topology on C(X)Ntantu, Ibula (Virginia Polytechnic Institute and State University, 1985)This paper investigates the compact-open topology on the set of Ck(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 Ck(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.
- On paracompactnessNtantu, Ibula (Virginia Polytechnic Institute and State University, 1982)This thesis is an investigation of the concept of paracompactness. It presents the history of paracompactness, analyzes this concept from several diverse points of view and tries to establish the relationship between these different views. The starting point is the work of Tukey [40]. The important problem of the metrization of topological spaces is presented as an application of the concept of paracompactness.