Representability of Certain Function Spaces
نویسندگان
چکیده
LetCp(X) be the space of all continuous real-valued functions on a space X , with the topology of pointwise convergence. In this paper we show thatCp(X) is not domain representable unless X is discrete for a class of spaces that includes all pseudo-radial spaces and all generalized ordered spaces. This is a first step toward our conjecture that if X is completely regular, then Cp(X) is domain representable if and only if X is discrete. In addition, we show that if X is completely regular and pseudonormal, then in the function space Cp(X), Oxtoby’s pseudocompleteness, strong Choquet completeness, and weak Choquet completeness are all equivalent to the statement “every countable subset of X is closed.” MR Subject Classifications: Primary = 54C35; Secondary = 54E52, 06B35, 05F30, 54F05.
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