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By Harold R. (-txt) Lutzer, G. Gierz, H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott


Fund. Math. 200 (2008), no. 2, 185–199.1730-6329 Summary: “Let Cp(X) be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) Cp(X) is Scott-domain representable; (b) Cp(X) is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal T1-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk that Cp(X) is subcompact if and only if X is discrete.

Topics: 4. J. de Groot, Subcompactness and the Baire category theorem, Indag. Math. 25 (1963, 761–767
Year: 2013
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