ABSTRACT
This chapter is about connectedness of a metric space. As usual, we start with the intuitive definition of connectedness and then develop relevant theory. Since most of the “remarkable” theorems on connectedness require the knowledge of continuous functions, we postpone these till Chapter 6, and throughout the chapter encourage the reader to think only geometrically and prove facts using the intuitive definition only. The chapter will also deal with some stronger concepts such as total disconnectedness. We give just an introduction as a kick-start to the concept, which will help the reader pursue general topology in the future.
