Variable Dimension Complexes, Part II : An Unified Approach to Some Combinatorial Lemmas in Topology (Classic Reprint)

Robert M. Freund

ISBN 10: 1332286445 / ISBN 13: 9781332286447

Published by Forgotten Books, 2015

About this Item

Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar.

Seller Inventory # 26101082/1

Bibliographic Details

• Title: Variable Dimension Complexes, Part II : An Unified Approach to Some Combinatorial Lemmas in Topology (Classic Reprint)
• Publisher: Forgotten Books
• Publication Date: 2015
• Language: English
• ISBN 10: 1332286445
• ISBN 13: 9781332286447
• Binding: Soft cover
• Condition: Hervorragend
• Seller catalogs:
  • Bücher

About this title

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.