Domain representability of $C_p\left(X\right)$

Harold Bennett, and David Lutzer. "Domain representability of $C_{p}(X)$." Fundamenta Mathematicae 200.2 (2008): 185-199. <http://eudml.org/doc/286297>.

@article{HaroldBennett2008,
abstract = {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.},
author = {Harold Bennett, David Lutzer},
journal = {Fundamenta Mathematicae},
keywords = {domain; Scott domain; Scott topology; domain representable space; pointwise convergence topology; normal space; pseudo-normal space; subcompact space; Choquet complete},
language = {eng},
number = {2},
pages = {185-199},
title = {Domain representability of $C_\{p\}(X)$},
url = {http://eudml.org/doc/286297},
volume = {200},
year = {2008},
}

TY - JOUR
AU - Harold Bennett
AU - David Lutzer
TI - Domain representability of $C_{p}(X)$
JO - Fundamenta Mathematicae
PY - 2008
VL - 200
IS - 2
SP - 185
EP - 199
AB - 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.
LA - eng
KW - domain; Scott domain; Scott topology; domain representable space; pointwise convergence topology; normal space; pseudo-normal space; subcompact space; Choquet complete
UR - http://eudml.org/doc/286297
ER -