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- 저자 : Arp´ad Sz´az (검색결과 2 건)
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Lower semicontinuity properties of relations in relator Spaces
Arp´ad Sz´az 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.1
After some preparations, we investigate uniform, proximal, and topological lower semicontinuity properties of arbitrary relations in relator spaces and linear relations in vector relator spaces.
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FOUNDATIONS OF THE THEORY OF VECTOR RELATORS
Arp´ad Sz´az 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.1
A nonvoid family R of binary relations on a nonvoid set X is called a relator on X. In particular, a relator R on a vector space X is called a vector relator on X if (1) R(x) = x + R(0) for all R ∈ R and x ∈ X;(2) R(0) is an absorbing balanced subset of X for all R ∈ R;(3) for each R ∈ R there exists S ∈ R such that S (0) + S (0) ⊂ R(0) . Vector relators are more convenient means than vector topologies. They are mainly motivated by the fact that if P is a nonvoid family of preseminorms on X,then the collection RP of all surroundings Bpr = { (x, y) : p (x − y) < r } , where p ∈ P and r > 0 , is a vector relator on X. Postulates (1) – (3) imply that R is a reflexive, symmetric, uniformly transitive and well-chained relator on X such that each member of R is a balanced translation relation. Moreover, it is also noteworthy that if in particular each member of P is a seminorm, then the members of RP are, in addition, convex. Therefore, before studying the most fundamental properties of vector relators,and the linearity properties of their induced basic tools, we shall briefly list some basic properties of translation, balanced and convex relations. Moreover, we shall greatly improve and supplement some relevant former results on relators.
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