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001-es BibID:	BIBFORM015991
Első szerző:	Száz Árpád (alkalmazott matematikus)
Cím:	Foundations of the theory of vector relators / Árpád Száz
Dátum:	2010
Megjegyzések:	A nonvoid family R of binary relations on a nonvoid set X is calleda relator on X . In particular, a relator R on a vector space X is called a vectorrelator 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 aremainly motivated by the fact that if P is a nonvoid family of preseminorms on X ,pthen the collection RP of all surroundings B r = { (x, y) : p (x ? y) < r } , wherep ? P and r > 0 , is a vector relator on X .Postulates (1) ? (3) imply that R is a reflexive, symmetric, uniformly transitiveand well-chained relator on X such that each member of R is a balanced translationrelation. Moreover, it is also noteworthy that if in particular each member of P is aseminorm, 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 somebasic properties of translation, balanced and convex relations. Moreover, we shallgreatly improve and supplement some relevant former results on relators.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban Translation and balanced relations Relators (families of relations) and their induced basic tools (interiors open and fat sets, and convergences). Refinements and classifications of relators Preseminorms and vector relators (alternatives for vector topologies)
Megjelenés:	Advanced Studies in Contemporary Mathematics (Kyungshang). - 20 (2010), p. 139-195. -
Pályázati támogatás:	NK 81402 OTKA
Internet cím:	Intézményi repozitóriumban (DEA) tárolt változat
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