scholarly journals Orthomodular lattices and closure operations in ordered vector spaces

2010 ◽  
Author(s):  
Jan Florek
Keyword(s):  
Vector Spaces ◽  
Orthomodular Lattices ◽  
Ordered Vector Spaces ◽  
Closure Operations

Fuzzy topological ordered vector spaces I

1993 ◽  
Vol 54 (2) ◽  
pp. 213-220 ◽  
Author(s):  
M.Y. Bakier ◽  
K. El-Saady
Keyword(s):  
Vector Spaces ◽  
Ordered Vector Spaces

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 $\mathbb{Q}$.

scholarly journals Nonsmooth analysis and optimization on partially ordered vector spaces

1992 ◽  
Vol 15 (1) ◽  
pp. 65-81 ◽  
Author(s):  
Thomas W. Reiland
Keyword(s):  
Vector Lattice ◽  
Vector Spaces ◽  
Range Space ◽  
Topological Vector Spaces ◽  
Complete Vector Lattice ◽  
Lipschitz Mappings ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces ◽  
Complete Vector ◽  
Locally Convex

Interval-Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz-type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice. Sample applications to the theory of nonsmooth optimization are given.

On Integration in Partially Ordered Groups

1983 ◽  
Vol 35 (2) ◽  
pp. 353-372 ◽  
Author(s):  
Panaiotis K. Pavlakos
Keyword(s):  
Vector Spaces ◽  
Order Structure ◽  
Topological Groups ◽  
Topological Vector Spaces ◽  
Lattice Group ◽  
Partially Ordered ◽  
Ordered Groups ◽  
Measurable Functions ◽  
Ordered Vector Spaces ◽  
Definition Of

M. Sion and T. Traynor investigated ([15]-[17]), measures and integrals having values in topological groups or semigroups. Their definition of integrability was a modification of Phillips-Rickart bilinear vector integrals, in locally convex topological vector spaces.The purpose of this paper is to develop a good notion of an integration process in partially ordered groups, based on their order structure. The results obtained generalize some of the results of J. D. M. Wright ([19]-[22]) where the measurable functions are real-valued and the measures take values in partially ordered vector spaces.Let if be a σ-algebra of subsets of T, X a lattice group, Y, Z partially ordered groups and m : H → F a F-valued measure on H. By F(T, X), M(T, X), E(T, X) and S(T, X) are denoted the lattice group of functions with domain T and with range X, the lattice group of (H, m)-measurable functions of F(T, X) and the lattice group of (H, m)-elementary measurable functions of F(T, X) and the lattice group of (H, m)-simple measurable functions of F(T, X) respectively.

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