Supsets on partially ordered topological linear spaces
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In this article, Supsets and infsets for subsets of a partially ordered topological linear space were introduced. And these notions generalize the usual notions of supremum and infimum in Riesz spaces.Abstract:
We introduce supsets and infsets for subsets of a partially ordered topological linear space. These notions generalize the usual notions of supremum and infimum in Riesz spaces. We shall investigate properties of supsets and infsets in this paper.read more
Citations
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Journal ArticleDOI
Vector superior and inferior
TL;DR: In this paper, order-conically compact ordered Hausdorff real topological vector spaces are introduced so that in such a space every nonempty bounded below (respectively, bounded above) set has a nonempty inferior set.
Journal ArticleDOI
On Supremal and Maximal Sets with Respect to Random Partial Orders
TL;DR: In this article, the authors deal with definition of supremal sets in a rather general framework where deterministic and random preference relations (preorders) and partial orders are defined by continuous multi-utility representations.
Journal ArticleDOI
Optimal Set in Ordered Linear Space
TL;DR: In this article, the authors introduced generalized supremum and infimam for a subset A of a partially ordered linear space E generalizing the notion of supremum in Riesz space.
Book ChapterDOI
On Supremal and Maximal Sets with Respect to Random Partial Orders
TL;DR: In this article, the authors define supremal sets in a general framework where deterministic and random preference relations (preorders) and partial orders are defined by continuous multi-utility representations.
Super-Lattice Partial Order Relations in Normed Linear Spaces
TL;DR: In this article, a class of partially ordered linear spaces, called super-lattices, are studied, where the lattice identities and properties of linear lattices are extended.
References
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Book
Banach Lattices and Positive Operators
TL;DR: In this paper, the authors propose the use of linear operators on positive matrices and apply it to non-positive matrices, including the case of positive projections. But they do not consider the case where positive projections are defined by a linear operator.
Book
Riesz Spaces, II
TL;DR: In this paper, the authors present a survey of L p Spaces and Compact Operators, including Orthomorphisms and f-Algebras, as well as Kernel Operators.