LEADER 04854oam 2200673 450 001 9910808180303321 005 20210114205012.0 010 $a1-118-40743-1 010 $a1-118-54874-4 010 $a1-118-54870-1 035 $a(CKB)2550000001108747 035 $a(EBL)1332520 035 $a(OCoLC)842307638 035 $a(SSID)ssj0000950019 035 $a(PQKBManifestationID)11520856 035 $a(PQKBTitleCode)TC0000950019 035 $a(PQKBWorkID)11003465 035 $a(PQKB)11771289 035 $a(DLC) 2013018014 035 $a(MiAaPQ)EBC1332520 035 $a(PPN)191455784 035 $a(EXLCZ)992550000001108747 100 $a20130501d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe elements of Cantor sets $ewith applications /$fRobert W. Vallin 205 $aFirst edition. 210 1$aHoboken, New Jersey :$cWiley,$d[2013] 215 $a1 online resource (248 p.) 300 $aDescription based upon print version of record. 311 $a1-118-40571-4 311 $a1-299-77582-9 320 $aIncludes bibliographical references and index. 327 $aCover; Title Page; Copyright Page; CONTENTS; Foreword; Preface; Acknowledgments; Introduction; 1 A Quick Biography of Cantor; 2 Basics; 2.1 Review; Exercises; 3 Introducing the Cantor Set; 3.1 Some Definitions and Basics; 3.2 Size of a Cantor Set; 3.2.1 Cardinality; 3.2.2 Category; 3.2.3 Measure; 3.3 Large and Small; Exercises; 4 Cantor Sets and Continued Fractions; 4.1 Introducing Continued Fractions; 4.2 Constructing a Cantor Set; 4.3 Diophantine Equations; 4.4 Miscellaneous; Exercises; 5 p-adic Numbers and Valuations; 5.1 Some Abstract Algebra; 5.2 p-adic Numbers 327 $a5.2.1 An Analysis Point of View5.2.2 An Algebra Point of View; 5.3 p-adic Integers and Cantor Sets; 5.4 p-adic Rational Numbers; Exercises; 6 Self-Similar Objects; 6.1 The Meaning of Self-Similar; 6.2 Metric Spaces; 6.3 Sequences in (S, d); 6.4 Affine Transformations; 6.5 An Application for an IFS; Exercises; 7 Various Notions of Dimension; 7.1 Limit Supremum and Limit Infimum; 7.2 Topological Dimension; 7.3 Similarity Dimension; 7.4 Box-Counting Dimension; 7.5 Hausdorff Measure and Dimension; 7.6 Miscellaneous Notions of Dimension; Exercises; 8 Porosity and Thickness-Looking at the Gaps 327 $a8.1 The Porosity of a Set8.2 Symmetric Sets and Symmetric Porosity; 8.3 A New and Different Definition of Cantor Set; 8.4 Thickness of a Cantor Set; 8.5 Applying Thickness; 8.6 A Bit More on Thickness; 8.7 Porosity in a Metric Space; Exercises; 9 Creating Pathological Functions via C; 9.1 Sequences of Functions; 9.2 The Cantor Function; 9.3 Space-Filling Curves; 9.4 Baire Class One Functions; 9.5 Darboux Functions; 9.6 Linearly Continuous Functions; Exercises; 10 Generalizations and Applications; 10.1 Generalizing Cantor Sets; 10.2 Fat Cantor Sets; 10.3 Sums of Cantor Sets 327 $a10.4 Differences of Cantor Sets10.5 Products of Cantor Sets; 10.6 Cantor Target; 10.7 Ana Sets; 10.8 Average Distance; 10.9 Non-Averaging Sets; 10.10 Cantor Series and Cantor Sets; 10.11 Liouville Numbers and Irrationality Exponents; 10.12 Sets of Sums of Convergent Alternating Series; 10.13 The Monty Hall Problem; 11 Epilogue; References; Index 330 $a"This book is a thorough introduction to the Cantor (Ternary) Set and its applications and brings together many of the topics (advanced calculus, probability, topology, and algebra) that mathematics students are required to study, but unfortunately are treated as separate ideas. This book successfully bridges the gap between how several mathematical fields interact using Cantor Sets as the common theme. While the book is mathematically self-contained, readers should be comfortable with mathematical formalism and have some experience in reading and writing mathematical proofs. Chapter coverage includes: a biography of Cantor; an introduction to the Cantor (Ternary) Set; Self-Similar Sets and Fractal Dimensions; sums of Cantor Sets; the role of Cantor Sets to create pathological functions; and additional topics such as continued fractions, Ana Sets, and p-adic numbers"--$cProvided by publisher. 606 $aCantor sets 606 $aMeasure theory 606 $aMathematical analysis 606 $aMATHEMATICS / Mathematical Analysis$2bisacsh 615 0$aCantor sets. 615 0$aMeasure theory. 615 0$aMathematical analysis. 615 7$aMATHEMATICS / Mathematical Analysis. 676 $a515.8 686 $aMAT034000$2bisacsh 700 $aVallin$b Robert W$01649137 801 0$bDLC 801 1$bDLC 801 2$bDLC 906 $aBOOK 912 $a9910808180303321 996 $aThe elements of Cantor sets$93997713 997 $aUNINA