Supplementary Exercises*: Nets: 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
If
, which is ordered and, therefore, by 1, is a directed set, then the net
is merely a sequence of points
and the definition of convergence is as follows:
iff for any neighborhood
of
there is
such that
implies
.