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

Hager, Anthony W., Kimber, Chawne M., and McGovern, Warren W.. "Unique $a$-closure for some $\ell $-groups of rational valued functions." Czechoslovak Mathematical Journal 55.2 (2005): 409-421. <http://eudml.org/doc/30954>.

@article{Hager2005,
abstract = {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 $C(X)$.},
author = {Hager, Anthony W., Kimber, Chawne M., McGovern, Warren W.},
journal = {Czechoslovak Mathematical Journal},
keywords = {archimedean lattice-ordered group; $a$-closure; rational-valued functions; zero-dimensional space; archimedean lattice-ordered group; -closure; rational-valued functions; zero-dimensional space},
language = {eng},
number = {2},
pages = {409-421},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unique $a$-closure for some $\ell $-groups of rational valued functions},
url = {http://eudml.org/doc/30954},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Hager, Anthony W.
AU - Kimber, Chawne M.
AU - McGovern, Warren W.
TI - Unique $a$-closure for some $\ell $-groups of rational valued functions
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 409
EP - 421
AB - 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 $C(X)$.
LA - eng
KW - archimedean lattice-ordered group; $a$-closure; rational-valued functions; zero-dimensional space; archimedean lattice-ordered group; -closure; rational-valued functions; zero-dimensional space
UR - http://eudml.org/doc/30954
ER -