Ebook: The Elements of Cantor Sets: With Applications

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.

Content:
Chapter 1 A Quick Biography of Cantor (pages 1–3):
Chapter 2 Basics (pages 5–15):
Chapter 3 Introducing the Cantor Set (pages 17–49):
Chapter 4 Cantor Sets and Continued Fractions (pages 51–66):
Chapter 5 P‐ADIC Numbers and Valuations (pages 67–89):
Chapter 6 Self‐Similar Objects (pages 91–117):
Chapter 7 Various Notions of Dimension (pages 119–141):
Chapter 8 Porosity and Thickness–Looking at the Gaps (pages 143–156):
Chapter 9 Creating Pathological Functions via C (pages 157–180):
Chapter 10 Generalizations and Applications (pages 181–215):
Chapter 11 Epilogue (page 217):