Supplementary Exercises*: Nets: Problem 8 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
If
then for any neighborhood
of
there is
such that
implies
. Since
is cofinal in J, there is
such that
. For all
,
, hence,
.