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(Ebook) Geometry of Convex Sets by I. E. Leonard, J. E. Lewis ISBN 9781119022664, 1119022665

  • SKU: EBN-5318554
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Authors:I. E. Leonard, J. E. Lewis
Pages:336 pages.
Year:2015
Editon:1
Publisher:Wiley
Language:english
File Size:1.89 MB
Format:pdf
ISBNS:9781119022664, 1119022665
Categories: Ebooks

Product desciption

(Ebook) Geometry of Convex Sets by I. E. Leonard, J. E. Lewis ISBN 9781119022664, 1119022665

A gentle introduction to the geometry of convex sets in n-dimensional space
Geometry of Convex Sets begins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets of n-dimensional space. Many properties of convex sets can be discovered using just the linear structure. However, for more interesting results, it is necessary to introduce the notion of distance in order to discuss open sets, closed sets, bounded sets, and compact sets. The book illustrates the interplay between these linear and topological concepts, which makes the notion of convexity so interesting.
Thoroughly class-tested, the book discusses topology and convexity in the context of normed linear spaces, specifically with a norm topology on an n-dimensional space.
Geometry of Convex Sets also features: 
  • An introduction to n-dimensional geometry including points; lines; vectors; distance; norms; inner products; orthogonality; convexity; hyperplanes; and linear functionals    
  • Coverage of n-dimensional norm topology including interior points and open sets; accumulation points and closed sets; boundary points and closed sets; compact subsets of n-dimensional space; completeness of n-dimensional space; sequences; equivalent norms; distance between sets; and support hyperplanes ·
  • Basic properties of convex sets; convex hulls; interior and closure of convex sets; closed convex hulls; accessibility lemma; regularity of convex sets; affine hulls; flats or affine subspaces; affine basis theorem; separation theorems; extreme points of convex sets; supporting hyperplanes and extreme points; existence of extreme points; Krein–Milman theorem; polyhedral sets and polytopes; and Birkhoff’s theorem on doubly stochastic matrices
  • Discussions of Helly’s theorem; the Art Gallery theorem; Vincensini’s problem; Hadwiger’s theorems; theorems of Radon and Caratheodory; Kirchberger’s theorem;
*Free conversion of into popular formats such as PDF, DOCX, DOC, AZW, EPUB, and MOBI after payment.

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