Section 33: 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
The distance between a point and a set was defined in §27. It was shown that it is continuous, and
iff
(exercise 2 of §27). Therefore, for two closed sets the expression is well-defined (the denominator is never 0), continuous and takes 0 on
, 1 on
.