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This is a study of the completeness properties of the space Cps(X) of continuous real-valued functions on a Tychonoff space X, where the function space has the pseudocompact-open topology. The properties range from complete metrizability to the Baire space property.
A metric space (X, d) is called an Atsuji space if every real-valued continuous function on (X, d) is uniformly continuous. It is well-known that an Atsuji space must be complete. A metric space (X, d) is said to have an Atsuji completion if its completion ( $$ \hat X $$ , d) is an Atsuji space. In this paper, we study twelve equivalent (external) characterizations for a metric space to have an...
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