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This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of 2 or 3 dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution to different problems in these spaces. 1957 edition.
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ISBN-10:  0486458466
ISBN-13:  978-0486458465
Author:  H. G. Eggleston
Publisher:  Dover Publications
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review by . June 23, 2010
The following definition of convexity is used in this book.    A subset X of R2 or R3 is convex if whenever x and y are in X the segment connecting them is also in X.    Using this definition, a series of problems are presented and solved. Organized by chapter, they are    Chapter 1) Problems in which convexity is used either by analogy or for subsidiary arguments  *) The intersection of connected open sets  *) Approximations …
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