Section 52: Problem 6 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Show that if
is path connected, the homomorphism induced by a continuous map is independent of base point, up to isomorphisms of the groups involved. More precisely, let
be continuous, with
and
. Let
be a path in
from
to
, and let
. Show that
This equation expresses the fact that the following diagram of maps “commutes.”