Supplementary Exercises*: Nets: Problem 4 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
Every neighborhood of
contains a basis neighborhood
. There are
and
such that
and
for all
and
. Since
is a net, there is
such that
implies both
and
. Therefore, "starting" from
all points
are in
.