4 CONNECTEDNESS
In the study of topological spaces and their application, a notion that is often useful is
connectedness.
Roughly speaking, a connected topological space is one where you can move from any point of the
space to another point without leaving the space. In this chapter, we give the precise definition
of a topological space and then present some basic properties of connected topological
spaces.
4.1 Definition and Examples of Connected Spaces
4.2 The Intermediate Value Theorem
4.3 Path-Connectedness
4.4 Practice Problems
4.2 The Intermediate Value Theorem
4.3 Path-Connectedness
4.4 Practice Problems
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