Elements of the Topology of Plane Sets of Points [Paperback]

This book provides an elementary introduction to the ideas and methods of topology.This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems and special attention is given to the results needed in the theory of functions.This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems and special attention is given to the results needed in the theory of functions.This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems and special attention is given to the results needed in the theory of functions.Preface to the second edition; 1. Sets; 2. Closed sets and open sets in metric spaces; 3. Homeomorphism and continuous mappings; 4. Connection; 5. Separation theorems; 6. Simply- and multiply-connected plane domains; 7. Homotopy properties; Notes; Index.