Section 18: 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
Show that the subspace
of
is homeomorphic with
and the subspace
of
is homeomorphic with
.
In both cases
works as a homeomorphism (I believe Munkres means
in both cases, especially in the second case). The inverse function is
. Both are continuous (as Munkres says, “these are familiar facts from calculus”).