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By Harold R. (-txt) Lutzer

Abstract

Domain representability of certain function spaces. (English summary) Topology Appl. 156 (2009), no. 11, 1937–1942. Summary: “Let Cp(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 that Cp(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 statemen

Topics: 4. J. de Groot, Subcompactness and the Baire category theorem, Indag. Math. (N.S.) 25 (1963) 761–767. MR0159303 (28 #2520
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.372.4295
Provided by: CiteSeerX
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