Section 54: Problem 8 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 covering map, with
path connected. Show that if
is simply connected, the
is a homeomorphism.
According to Theorem 54.4,
is surjective, hence,
, and using Exercise 3 of Section 53,
is a bijective covering map (continuous and open).