Section 3: Problem 1 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 two points
and
of the plane to be equivalent if
. Check that this is an equivalence relation and describe the equivalence classes.
Reflexivity, Symmetry and Transitivity (RST) obviously hold. The equivalence classes are sets of points on parabolas
.