**Massey Exercise 2.3.2**

Suppose that for any two points , all path classes from to induce the same isomorphism .
From the last exercise, we see that any two paths in the space (between *any* points because and are arbitrary), must have the property that is in the center of .
But, any loop in can be considered as the product of a path to some other point and its inverse.
So, every member of is in the center.
That is, the fundamental group of must be abelian.