# On Some Infinite Convex Invariants

 dc.contributor.author Vijayakrishnan,S dc.contributor.author Chakravarthi,R S dc.contributor.author Thrivikraman,T dc.date.accessioned 2008-07-05T09:45:39Z dc.date.available 2008-07-05T09:45:39Z dc.date.issued 2002 dc.identifier.uri http://dyuthi.cusat.ac.in/purl/89 dc.description.abstract The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the en_US classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions dc.language.iso en en_US dc.publisher Department of Mathematics,Faculty OF Science en_US dc.subject Infinite convex invariants en_US dc.subject Axioms en_US dc.subject Convexity theory en_US dc.subject Helly dependence en_US dc.subject Helly numbers en_US dc.subject Transfinite convex dimension en_US dc.title On Some Infinite Convex Invariants en_US dc.type Thesis en_US
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