Domain representability of Cp(X)
Harold Bennett ; David Lutzer
Fundamenta Mathematicae, Tome 201 (2008), p. 185-199 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:286297 
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     title = {Domain representability of $C\_{p}(X)$
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     journal = {Fundamenta Mathematicae},
     volume = {201},
     year = {2008},
     pages = {185-199},
     zbl = {1152.54016},
     language = {en},
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Harold Bennett; David Lutzer. Domain representability of $C_{p}(X)$
            . Fundamenta Mathematicae, Tome 201 (2008) pp. 185-199. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-2-5/