TY - JOUR

T1 - Domain-representability of certain complete spaces

AU - Bennett, Harold

AU - Lutzer, David

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - In this paper we show that three major classes of topological spaces are domain-representable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: (i) T3 subcompact spaces, (ii) strongly α- favorable spaces (with stationary strategies) that have either a G δ-diagonal or a base of countable order, and (iii) complete quasi-developable T3-spaces. It follows that any regular space with a monotonically complete base of countable order (in the sense of Wicke and Worrell) is domain-representable, as is any space with exactly one limit point. (In fact, any space with exactly one limit point is domain representable using a Scott domain.) The result on strongly a-favorable spaces (with stationary strategies) that have a Gδ-diagonal can be used to show that spaces such as the Sorgenfrey line, the Michael line, the Moore plane, the Nagata plane, and Heath's V-space are domain-representable, and to show that a domain-representable space can be Hausdorff but not regular.

AB - In this paper we show that three major classes of topological spaces are domain-representable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: (i) T3 subcompact spaces, (ii) strongly α- favorable spaces (with stationary strategies) that have either a G δ-diagonal or a base of countable order, and (iii) complete quasi-developable T3-spaces. It follows that any regular space with a monotonically complete base of countable order (in the sense of Wicke and Worrell) is domain-representable, as is any space with exactly one limit point. (In fact, any space with exactly one limit point is domain representable using a Scott domain.) The result on strongly a-favorable spaces (with stationary strategies) that have a Gδ-diagonal can be used to show that spaces such as the Sorgenfrey line, the Michael line, the Moore plane, the Nagata plane, and Heath's V-space are domain-representable, and to show that a domain-representable space can be Hausdorff but not regular.

UR - http://www.scopus.com/inward/record.url?scp=55949104092&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:55949104092

VL - 34

SP - 753

EP - 772

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

SN - 0362-1588

IS - 3

ER -