Section 3: Problem 2 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
Let
be a relation on a set
. If
, define the restriction of
to
to be the relation
. Show that the restriction of an equivalence relation is an equivalence relation.
RST hold for the restriction of
(follows directly from their definitions restricted to the subset; all three properties hold because the restriction includes all pairs in
that have both elements in the subset), and the equivalence classes are those of
intersected with the subset.