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Introduction to Closure Systems

Robert E. Jamison (Autor)

Buch | Hardcover

352 Seiten

2021
Crc Press Inc (Verlag)
978-1-4398-1991-3 (ISBN)

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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.

Robert E. Jamison, Clemson University, South Carolina, USA

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

Erscheint lt. Verlag	1.1.2021
Reihe/Serie	Discrete Mathematics and Its Applications
Zusatzinfo	100 Illustrations, black and white
Verlagsort	Bosa Roca
Sprache	englisch
Maße	156 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-4398-1991-2 / 1439819912
ISBN-13	978-1-4398-1991-3 / 9781439819913
Zustand	Neuware