Section 6: 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

Show that if $B$ is not finite and $B\subset A$ , then $A$ is not finite.

Using Corollary 6.6, if $A$ were finite, $B$ would be finite too. Or, alternatively, using Corollary 6.7, if $A$ is finite, then there is an injective function from $A$ into a section of the positive integers, and the restriction of the function on $B$ is an injective function from $B$ into a section of the positive integers. Contradiction.

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Section 6: Problem 2 Solution

Section 6: Problem 2 Solution