Section 3: Problem 6 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
Define a relation on the plane by setting
if either
, or
and
. Show that this is an order relation on the plane, and describe it geometrically.
iff
lies on a lower parabola
or on the same parabola, but to the left of
. Comparability, Nonreflexivity and Transitivity (CnRT) hold.