Section 3: Problem 7 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 the restriction of an order relation is an order relation.
CnRT hold for the restriction. Nonreflexivity holds because the restriction does not add any new pairs of points, and Comparability and Transitivity hold because the restriction includes all pairs of the initial relation such that both elements belong to the subset.