Section 9: Problem 4 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

There was a theorem in §7 whose proof involved an infinite number of arbitrary choices. Which one was it? Rewrite the proof so as to make explicit the use of the choice axiom. (Several of the earlier exercises have used the choice axiom also.)

Theorem 7.5. We must consider the collection of the sets $F_{n}$ of all surjective functions from $\mathbb{Z}_{+}$ onto $A_{n}$ , and the set $F$ of all surjective functions from $\mathbb{Z}_{+}$ onto $J$ , and choose one function from each set of the collection.

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Section 9: Problem 4 Solution

Section 9: Problem 4 Solution