Example 1: C[a,b] is the set of continuous functions y=y(x) on [a,b]. To be able to compare different functions we need to define a norm on the space. We can for instance use
Example 3: The spaces Cn[a,b], n=2,3,… ar defined in a corresponding way.
<>Given a specific norm, we get the distance d(y1,y2) between two functions y1 and y2 as