Section 29: 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 one-point compactification of
is homeomorphic with
.
is a well-ordered set, hence, it satisfies the least upper bound property (Exercise 10.1), and is compact (Theorem 27.1) and Hausdorff (Theorem 17.11), and adds just 1 point to
(which is Hausdorff and locally compact, Example 3, page 183, but not compact, though limit point compact, Example 2, page 179).