Section 24: Problem 2 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
Example 6 of §18 proves that
is connected. Let
be the continuous function
(§21). For any
:
, therefore, by the Intermediate Value Theorem, there is
such that
or
.