3Connectivity

IB Metric and Topological Spaces

3 Connectivity

Finally we can get to something more interesting. In this chapter, we will study

the connectivity of spaces. Intuitively, we would want to say that a space is

“connected” if it is one-piece. For example,

R

is connected, while

R \ {

0

}

is

not. We will come up with two different definitions of connectivity - normal

connectivity and path connectivity, where the latter implies the former, but not

the other way round.