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Introduction to Closure Systems: (Discrete Mathematics and Its Applications)

Introduction to Closure Systems: (Discrete Mathematics and Its Applications)


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About the Book

The notion of closure pervades mathematics, especially in the fields of topology and projective geometry. Demonstrating this pervasiveness in the field, this graduate-level book provides a complete introduction to closure systems. With an emphasis on finite spaces and algebraic closures, the text covers graph theory, ordered sets, lattices, projective geometry, and formal logic as they apply to the study of closures. Each chapter presents a vignette to illustrate the topic covered. The author also includes numerous exercises as well as concrete examples to support the material discussed.

Table of Contents:
Preface An Introduction to Closures Six Motivating Examples Some Properties of Set Maps A Budget of Closures Arity Interval Functions 1 3-letter Scrabble Some More Algebraic Examples Napoleonic Closure Universality of Napoleonic Closure Basic Properties of Closures Closures Systems and Their Hulls Hull Operators and the Substitution Property Filling in Dependencies Algebraic and Topological Closures Closures That Are Both Topological and Algebraic Isomorphism and Cryptomorphy Separation Constructions on Closures Small Closures Alignments Universal Algebras Realizing Alignments by a Single Operation Universality of Groupoids Universality of Napoleonic Closure Copoints in Finitary Closures Copoints and the Separation Axioms 53 and 54 Matroids and Antimatroids Independence More Examples of Matroids and Antimatroids Order Convexity Acyclic Semigroups Articulated Sums Background Review Functions Relations Orders Basic Graph Theory Some More Algebraic Examples Two Binary Operations Set Theory Cardinals The Axiom of Choice Ordinals Countability

About the Author :
Robert E. Jamison, Clemson University, South Carolina, USA


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Product Details
  • ISBN-13: 9781439819920
  • Publisher: Taylor & Francis Inc
  • Publisher Imprint: CRC Press Inc
  • Language: English
  • No of Pages: 352
  • ISBN-10: 1439819920
  • Publisher Date: 15 Jun 2017
  • Binding: Digital (delivered electronically)
  • No of Pages: 352
  • Series Title: Discrete Mathematics and Its Applications


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