Section 35*: 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
Take the continuous function on the union of two disjoint closed sets equal to 1 for one set and 0 for the other set (it is continuous because both sets are closed and, therefore, open in the union) and extend it continuously on
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