Section 31: Problem 5 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 $f,g:X\to Y$ be continuous; assume that $Y$ is Hausdorff. Show that $\{x|f(x)=g(x)\}$ is closed in X.

The set is the preimage of the diagonal of $Y\times Y$ (which is closed as $Y$ is Hausdorff) under the continuous (Theorem 19.6) function $x\to(f(x),g(x))$ .

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Section 31: Problem 5 Solution

Section 31: Problem 5 Solution