Domain representability of $C_{p}(X)$

• Autorzy: Harold Bennett , David Lutzer
• Języki publikacji: EN

Abstrakty

EN

Let $C_{p}(X)$ 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) $C_{p}(X)$ is Scott-domain representable; (b) $C_{p}(X)$ 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 $C_{p}(X)$ is subcompact if and only if X is discrete.

Kategorie tematyczne

• 06B35: Continuous lattices and posets, applications
• 54E52: Baire category, Baire spaces
• 54C35: Function spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 200
• Numer: 2
• Strony: 185-199

Daty

wydano

2008

Twórcy

autor

Harold Bennett

• Mathematics Department, Texas Tech University, Lubbock, TX 79409, U.S.A.

autor

David Lutzer

• Mathematics Department, College of William and Mary, Williamsburg, VA 23187-8795, U.S.A.

Identyfikatory

DOI

10.4064/fm200-2-5