Section 26: 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
(a) If
is compact then
is compact.(b) Suppose one is finer than the other. Then the identity mapping from the finer one to the coarser one is a continuous and bijective function that maps a compact space to a Hausdorff space. Therefore, it is a homeomorphism and the topologies are the same.