A systematic and integrated approach to Cantor Sets and theirapplications to various branches of mathematics
The Elements of Cantor Sets: With Applications features athorough introduction to Cantor Sets and applies these sets as abridge between real analysis, probability, topology, andalgebra.
The author fills a gap in the current literature by providing anintroductory and integrated perspective, thereby preparing readersfor further study and building a deeper understanding of analysis, topology, set theory, number theory, and algebra.
The Elements of Cantor Sets provides coverage of:
- Basic definitions and background theorems as well ascomprehensive mathematical details
- A biography of Georg Ferdinand Ludwig Philipp Cantor, one ofthe most significant mathematicians of the last century
- Chapter coverage of fractals and self-similar sets, sums ofCantor Sets, the role of Cantor Sets in creating pathologicalfunctions, p-adic numbers, and several generalizations ofCantor Sets
- A wide spectrum of topics from measure theory to the Monty HallProblem
An ideal text for courses in real analysis, topology, algebra, and set theory for undergraduate and graduate-level courses withinmathematics, computer science, engineering, and physicsdepartments, The Elements of Cantor Sets is also appropriateas a useful reference for researchers and secondary mathematicseducation majors.