Section 17: 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 $A$ is closed in $Y$ and $Y$ is closed in $X$ , then $A$ is closed in $X$ .

If $Y$ is closed in $X$ , then we have $A$ is closed in $Y$ iff $A=Y\cap B$ for some $B$ closed in $X$ iff $A\subset Y$ and $A$ is closed in $X$ .

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Section 17: Problem 2 Solution

Section 17: Problem 2 Solution