Elements of Cantor Sets With Applications

Name: Elements of Cantor Sets With Applications
Price: 87.64 USD
Availability: InStock
ISBN: 9781118405710

ISBN-10: 1118405714

ISBN-13: 9781118405710

Edition: 2013

Authors: Robert W. Vallin

List price: $178.95

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Description:

This book uniquely provides a systematic and integrated approach to Cantor Sets, which play a central role in various branches of mathematics including advanced calculus, probability, topology, and algebra. Chapter coverage includes a biography of Cantor; an introduction to the Cantor (Ternary) Set; fractional dimensional objects; sums of Cantor Sets; the role of Cantor Sets to create functions; and additional topics such as Ana Sets and p-adic numbers. It gives readers a deeper understanding of real analysis and prepares them for further reading in probability and fractal geometry.

Book details

List price: $178.95
Copyright year: 2013
Publisher: John Wiley & Sons, Limited
Publication date: 7/3/2013
Binding: Hardcover
Pages: 256
Size: 6.35" wide x 9.55" long x 0.75" tall
Weight: 1.034
Language: English



Foreword


Preface


Acknowledgments


Introduction



A Quick Biography of Cantor



Basics



Review


Exercises



Introducing the Cantor Set



Some Definitions and Basics



Size of a Cantor Set



Cardinality



Category



Measure



Large and Small


Exercises



Cantor Sets and Continued Fractions



Introducing Continued Fractions



Constructing a Cantor Set



Diophantine Equations



Miscellaneous


Exercises



p-adic Numbers and Valuations



Some Abstract Algebra



p-adic Numbers



An Analysis Point of View



An Algebra Point of View



p-adic Integers and Cantor Sets



p-adic Rational Numbers


Exercises



Self-Similar Objects



The Meaning of Self-Similar



Metric Spaces



Sequences in (S, d)



Affine Transformations



An Application for an IFS


Exercises



Various Notions of Dimension



Limit Supremum and Limit Infimum



Topological Dimension



Similarity Dimension



Box-Counting Dimension



Hausdorff Measure and Dimension



Miscellaneous Notions of Dimension


Exercises



Porosity and Thickness-Looking at the Gaps



The Porosity of a Set



Symmetric Sets and Symmetric Porosity



A New and Different Definition of Cantor Set



Thickness of a Cantor Set



Applying Thickness



A Bit More on Thickness



Porosity in a Metric Space


Exercises



Creating Pathological Functions via C



Sequences of Functions



The Cantor Function



Space-Filling Curves



Baire Class One Functions



Darboux Functions



Linearly Continuous Functions


Exercises



Generalizations and Applications



Generalizing Cantor Sets



Fat Cantor Sets



Sums of Cantor Sets



Differences of Cantor Sets



Products of Cantor Sets



Cantor Target



Ana Sets



Average Distance



Non-Averaging Sets



Cantor Series and Cantor Sets



Liouville Numbers and Irrationality Exponents



Sets of Sums of Convergent Alternating Series



The Monty Hall Problem



Epilogue


References


Index