Imre Barany, Renyi Institute of Mathematics, Budapest, Hungary, and University College London, United Kingdom.
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Description
Basic concepts Caratheodory's theorem Radon's theorem Topological Radon Tverberg's theorem General position Helly's theorem Applications of Helly's theorem Fractional Helly Colourful Caratheodory Colourful Caratheodory again Colourful Helly Tverberg's theorem again Colourful Tverberg theorem Sarkaria and Kirchberger generalized The Erdos-Szekers theorem The same type lemma Better bound for the Erdos-Szekeres number Covering number, planar case The stretched grid Covering number, general case Upper bound on the covering number The point selection theorem Homogeneous selection Missing few simplices Weak $\varepsilon$-nets Lower bound on the size of weak $\varepsilon$-nets The $(p,q)$ theorem The colourful $(p,q)$ theorem $d$-intervals Halving lines, havling planes Convex lattice sets Fractional Helly for convex lattice sets Bibliography Index
This is an elegant, well written, concise treatment of an attractive and active subject, written by an expert who has made important contributions to the area himself. I am sure this will be a successful textbook."" -Noga Alon, Princeton University and Tel Aviv University ""I think this book is a gem."" -Janos Pach, Renyi Institute of Mathematics, Budapest