Section 35*: Problem 5 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
(a)
can be extended to a continuous
, then
such that
is continuous (in the product topology).(b) If
is continuous, and
is a homeomorphism such that
is a retract of
then there is a retraction
and
can be extended to a continuous function
. Then
is continuous.