Separation Theorem In The Plane

  • Dr. Jyoti .

Abstract

There are several difficult questions concerning the topology of the plane that arise quite naturally in the study of analysis. The answers to these questions seem geometrically quite obvious but turn out to be surprisingly hard to prove. They include the Jordan curve theorem, the Brouwer theorem on invariance of domain, and the classical theorem that the winding number of a simple closed curve is zero or 1. We prove them in this chapter as consequences of our study of covering spaces and the fundamental group

Published
2019-11-15
Section
Articles