#### Title

Measurements and G(delta)-Subsets of Domains

#### Document Type

Article

#### Department/Program

Mathematics

#### Journal Title

Canadian Mathematical Bulletin-Bulletin Canadien DE Mathematiques

#### Pub Date

2011

#### Volume

54

#### Issue

2

#### First Page

193

#### Abstract

In this paper we study domains, Scott domains, and the existence of measurements. We use a space created by D. K. Burke to show that there is a Scott domain P for which max(P) is a G(delta)-subset of P and yet no measurement mu on P has ker(mu) = max(P). We also correct a mistake in the literature asserting that [0, omega(1)) is a space of this type. We show that if P is a Scott domain and X subset of max(P) is a G(delta)-subset of P, then X has a G(delta)-diagonal and is weakly developable. We show that if X subset of max(P) is a G(delta)-subset of P, where P is a domain but perhaps not a Scott domain, then X is domain-representable, first-countable, and is the union of dense, completely metrizable subspaces. We also show that there is a domain P such that max(P) is the usual space of countable ordinals and is a G(delta)-subset of Pin the Scott topology Finally we show that the kernel of a measurement on a Scott domain can consistently be a normal, separable, non-metrizable Moore space.

#### Recommended Citation

Bennett, Harold and Lutzer, David, Measurements and G(delta)-Subsets of Domains (2011). *Canadian Mathematical Bulletin-Bulletin Canadien DE Mathematiques*, 54(2), 193-206.

10.4153/CMB-2010-104-3

#### DOI

10.4153/CMB-2010-104-3