Characterizations of the completely regular topological spacesX for whichC(X) is a dual ordered vector space

1983 ◽  
Vol 183 (3) ◽  
pp. 413-418 ◽  
Author(s):  
Hong-Yun Xiong
Keyword(s):  
Vector Space ◽  
Completely Regular ◽  
Ordered Vector Space

scholarly journals FINITE-DIMENSIONAL ORDERED VECTOR SPACES WITH RIESZ INTERPOLATION AND EFFROS–SHEN’S UNIMODULARITY CONJECTURE

2016 ◽  
Vol 101 (2) ◽  
pp. 277-287
Author(s):  
AARON TIKUISIS
Keyword(s):  
Vector Space ◽  
Inductive Limit ◽  
Space Structure ◽  
Vector Spaces ◽  
Ordered Vector Space ◽  
Finite Dimensional ◽  
Ordered Vector Spaces

It is shown that, for any field $\mathbb{F}\subseteq \mathbb{R}$, any ordered vector space structure of $\mathbb{F}^{n}$ with Riesz interpolation is given by an inductive limit of a sequence with finite stages $(\mathbb{F}^{n},\mathbb{F}_{\geq 0}^{n})$ (where $n$ does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with $\mathbb{F}$ replaced by the integers, $\mathbb{Z}$. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with $\mathbb{Q}$.

On sufficient condition for the Egoroff theorem of an ordered vector space-valued non-additive measure

2010 ◽  
Vol 161 (22) ◽  
pp. 2919-2922 ◽  
Author(s):  
Toshikazu Watanabe
Keyword(s):  
Vector Space ◽  
Sufficient Condition ◽  
Additive Measure ◽  
Ordered Vector Space

The order-bound topology

1972 ◽  
Vol 71 (2) ◽  
pp. 321-327 ◽  
Author(s):  
Yau-Chuen Wong
Keyword(s):  
Vector Space ◽  
Positive Cone ◽  
Order Topology ◽  
Bounded Subset ◽  
Partially Ordered ◽  
Convex Topology ◽  
Ordered Vector Space ◽  
Partially Ordered Vector Space ◽  
Locally Convex Topology ◽  
Locally Convex

Let (E, C) be a partially ordered vector space with positive cone C. The order-bound topology Pb(6) (order topology in the terminology of Schaefer(9)) on E is the finest locally convex topology for which every order-bounded subset of E is topologically bounded.

A note on measures with values in a partially ordered vector space

Positivity ◽  
2004 ◽  
Vol 8 (4) ◽  
pp. 395-400 ◽  
Author(s):  
Thierry Coquand
Keyword(s):  
Vector Space ◽  
Partially Ordered ◽  
Ordered Vector Space ◽  
Partially Ordered Vector Space

scholarly journals Subdifferentiability of Convex Functions with Values in an Ordered Vector Space.

1974 ◽  
Vol 34 ◽  
pp. 69 ◽  
Author(s):  
Jochem Zowe
Keyword(s):  
Vector Space ◽  
Convex Functions ◽  
Ordered Vector Space
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