scholarly journals The Geometric Interior in Real Linear Spaces

2010 ◽  
Vol 18 (3) ◽  
pp. 185-188 ◽  
Author(s):  
Karol Pąk
Keyword(s):  
Simplicial Complexes ◽  
Centre Of Mass ◽  
Linear Spaces ◽  
Real Linear ◽  
Abstract Simplicial Complexes

The Geometric Interior in Real Linear Spaces We introduce the notions of the geometric interior and the centre of mass for subsets of real linear spaces. We prove a number of theorems concerning these notions which are used in the theory of abstract simplicial complexes.

scholarly journals Sperner's Lemma

2010 ◽  
Vol 18 (4) ◽  
pp. 189-196 ◽  
Author(s):  
Karol Pąk
Keyword(s):  
Simplicial Complexes ◽  
Barycentric Subdivision ◽  
Arbitrary Vertex ◽  
Linear Spaces ◽  
Sperner’S Lemma ◽  
Real Linear

Sperner's Lemma In this article we introduce and prove properties of simplicial complexes in real linear spaces which are necessary to formulate Sperner's lemma. The lemma states that for a function ƒ, which for an arbitrary vertex υ of the barycentric subdivision B of simplex K assigns some vertex from a face of K which contains υ, we can find a simplex S of B which satisfies ƒ(S) = K (see [10]).

On the Intrinsic Core of Convex Cones in Real Linear Spaces

2021 ◽  
Vol 31 (2) ◽  
pp. 1276-1298
Author(s):  
Bahareh Khazayel ◽  
Ali Farajzadeh ◽  
Christian Günther ◽  
Christiane Tammer
Keyword(s):  
Convex Cones ◽  
Linear Spaces ◽  
Real Linear

scholarly journals Nearly directed subspaces of partially ordered linear spaces

1968 ◽  
Vol 16 (2) ◽  
pp. 135-144
Author(s):  
G. J. O. Jameson
Keyword(s):  
Linear Space ◽  
Transitive Relation ◽  
Linear Spaces ◽  
Real Linear Space ◽  
Partially Ordered ◽  
Real Linear ◽  
Image Position ◽  
Ordered Linear Spaces

Let X be a partially ordered linear space, i.e. a real linear space with a reflexive, transitive relation ≦ such that

scholarly journals ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhi-Ang Zhou
Keyword(s):  
Saddle Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Saddle Points ◽  
Linear Spaces ◽  
Equivalent Characterization ◽  
Generalized Cone Subconvexlikeness ◽  
Real Linear ◽  
The Relationship

We studyϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization ofϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between theϵ-Henig saddle point of the Lagrangian set-valued map and theϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.

scholarly journals Multilinear Operator and Its Basic Properties

2019 ◽  
Vol 27 (1) ◽  
pp. 35-45
Author(s):  
Kazuhisa Nakasho
Keyword(s):  
Algebraic Structure ◽  
Multilinear Operator ◽  
Multilinear Operators ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Basic Properties ◽  
Normed Linear Spaces ◽  
Real Linear

Summary In the first chapter, the notion of multilinear operator on real linear spaces is discussed. The algebraic structure [2] of multilinear operators is introduced here. In the second chapter, the results of the first chapter are extended to the case of the normed spaces. This chapter shows that bounded multilinear operators on normed linear spaces constitute the algebraic structure. We referred to [3], [7], [5], [6] in this formalization.

scholarly journals Semiconvex geometry

1981 ◽  
Vol 30 (4) ◽  
pp. 496-510 ◽  
Author(s):  
Joe Flood
Keyword(s):  
Algebraic Variety ◽  
Convex Sets ◽  
Convex Geometry ◽  
Algebraic Approach ◽  
Algebraic Proof ◽  
Linear Spaces ◽  
Structural Decomposition ◽  
Banach Theorem ◽  
Real Linear ◽  
Convex Subsets

AbstractSemiconvex sets are objects in the algebraic variety generated by convex subsets of real linear spaces. It is shown that the fundamental notions of convex geometry may be derived from an entirely algebraic approach, and that conceptual advantages result from applying notions derived from algebra, such as ideals, to convex sets. Some structural decomposition results for semiconvex sets are obtained. An algebraic proof of the algebraic Hahn-Banach theorem is presented.

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