Domain-representable spaces

Harold Bennett, and David Lutzer. "Domain-representable spaces." Fundamenta Mathematicae 189.3 (2006): 255-268. <http://eudml.org/doc/283149>.

@article{HaroldBennett2006,
abstract = {We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if X is domain-representable, then so is any $G_\{δ\}$-subspace of X. It follows that any Čech-complete space is domain-representable. These results answer several questions in the literature.},
author = {Harold Bennett, David Lutzer},
journal = {Fundamenta Mathematicae},
keywords = {continuous dcpo; domain; Scott domain; Baire space; Choquet-complete space; Michael line; Sorgenfrey line; ordinal space; -subspace; Čech-complete space},
language = {eng},
number = {3},
pages = {255-268},
title = {Domain-representable spaces},
url = {http://eudml.org/doc/283149},
volume = {189},
year = {2006},
}

TY - JOUR
AU - Harold Bennett
AU - David Lutzer
TI - Domain-representable spaces
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 3
SP - 255
EP - 268
AB - We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if X is domain-representable, then so is any $G_{δ}$-subspace of X. It follows that any Čech-complete space is domain-representable. These results answer several questions in the literature.
LA - eng
KW - continuous dcpo; domain; Scott domain; Baire space; Choquet-complete space; Michael line; Sorgenfrey line; ordinal space; -subspace; Čech-complete space
UR - http://eudml.org/doc/283149
ER -