Section 52: Problem 4 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
Let
; suppose
is a continuous map such that
for each
. (The map
is called a retraction of
onto
.) If
, show that
is surjective.
By definition,
, so if
, i.e.
is a loop in
based at
, then
, and
.