Section 6: Problem 3 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

Let $X$ be the two-element set $\{0,1\}$ . Find a bijective correspondence between $X^{\omega}$ and a proper subset of itself.

$f(x_{1},x_{2},...)=(0,x_{1},x_{2},...)$ is a bijective correspondence between the set of all $\{0,1\}$ -sequences and those starting with $0$ .

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Section 6: Problem 3 Solution

Section 6: Problem 3 Solution