The compact-open topology on C(X)
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Date
1985
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Virginia Polytechnic Institute and State University
Abstract
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.