Section 17: Problem 10 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
Show that every order topology is Hausdorff.
If
then either there is some
such that
and
and
are disjoint neighborhoods of
and
, respectively, or there is no element between
and
, so that
and
are disjoint neighborhoods of
and
, respectively.