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kharazishvili introduction combinatorial methods geometry 2024

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Textbook in PDF format Preface The index of an isometric embedding Maximal ot-subsets of the Euclidean plane The cardinalities of at-sets in a real Hilbert space Isosceles triangles and it-sets in Euclidean space Some geometric consequences of Ramsey’s combinatorial theorem Convexly independent subsets of infinite sets of points Homogeneous coverings of the Euclidean plane Three-colorings of the Euclidean plane and associated triangles of a prescribed type Chromatic numbers of graphs associated with point sets in Euclidean space The Szemerédi–Trotter theorem and its applications Minkowski’s theorem, number theory, and nonmeasurable sets Tarski’s plank problem Borsuk’s conjecture Piecewise affine approximations of continuous functions of several variables and Caratheodory–Gale polyhedra Dissecting a square into triangles of equal areas Geometric realizations of finite and infinite families of sets A geometric form of the Axiom of Choice Convex sets in real vector spaces Real-valued convex functions The Principle of Inclusion and Exclusion The Erdös–Mordell inequality Some facts from graph theory Bibiliography Index

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kharazishvili introduction combinatorial methods geometry 2024