Synopsis
This book provides constructive algorithms in combinatorial topology. It presents a unified approach to several combinatorial lemmas used in many branches of pure and applied mathematics. The author uses the path-following theory of labelled V-complexes to construct combinatorial proofs of a variety of combinatorial lemmas in topology. The book goes on to demonstrate two new dual lemmas on the n-dimensional cube, and uses a Generalized Sperner Lemma to prove a generalization of the Knaster–Kuratowski–Mazurkiewicz Covering Lemma on the simplex. The author also shows that Tucker's lemma can be derived directly from the Borsak–Ulam Theorem, and reports the interrelationships between these results, Brouwer’s Fixed Point Theorem, the Borsak–Ulam Theorem, the existence of stationary points on the simplex, and two new theorems on the simplex relating to the Generalized Covering Theorem. The book is of interest to researchers in the fields of topology, optimization, game theory, and mathematical economics.
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Variable Dimension Complexes, Part II (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book provides constructive algorithms in combinatorial topology. It presents a unified approach to several combinatorial lemmas used in many branches of pure and applied mathematics. The author uses the path-following theory of labelled V-complexes to construct combinatorial proofs of a variety of combinatorial lemmas in topology. The book goes on to demonstrate two new dual lemmas on the n-dimensional cube, and uses a Generalized Sperner Lemma to prove a generalization of the Knasterâ"Kuratowskiâ"Mazurkiewicz Covering Lemma on the simplex. The author also shows that Tucker's lemma can be derived directly from the Borsakâ"Ulam Theorem, and reports the interrelationships between these results, Brouwerâs Fixed Point Theorem, the Borsakâ"Ulam Theorem, the existence of stationary points on the simplex, and two new theorems on the simplex relating to the Generalized Covering Theorem. The book is of interest to researchers in the fields of topology, optimization, game theory, and mathematical economics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332286447_0
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Variable Dimension Complexes, Part II An Unified Approach to Some Combinatorial Lemmas in Topology Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332286447
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Variable Dimension Complexes, Part II An Unified Approach to Some Combinatorial Lemmas in Topology Classic Reprint
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Variable Dimension Complexes, Part II : An Unified Approach to Some Combinatorial Lemmas in Topology (Classic Reprint)
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