Section 55: Problem 1 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 a retract of
, then every continuous map
has a fixed point.
Let
be the retract,
be the inclusion map (
for
), then the continuous function
has a fixed point
(Theorem 55.6), implying
,
, and
.