Unique $a$-closure for some $\ell$-groups of rational valued functions

Title:

Unique $a$-closure for some $\ell$-groups of rational valued functions

Creator:

Hager, Anthony W., Kimber, Chawne M., and McGovern, Warren G.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3185974f-669c-40fd-bf24-72a72fc1f191
uuid:3185974f-669c-40fd-bf24-72a72fc1f191

Subject:

archimedean lattice-ordered group, $a$-closure, rational-valued functions, and zero-dimensional space

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Usually, an abelian $\ell $-group, even an archimedean $\ell $-group, has a relatively large infinity of distinct $a$-closures. Here, we find a reasonably large class with unique and perfectly describable $a$-closure, the class of archimedean $\ell $-groups with weak unit which are “$\mathbb Q$-convex”. ($\mathbb Q$ is the group of rationals.) Any $C(X,\mathbb Q)$ is $\mathbb Q$-convex and its unique $a$-closure is the Alexandroff algebra of functions on $X$ defined from the clopen sets; this is sometimes $C(X)$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

409-421

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:2

Harvested from:

CDK

Metadata only:

false