Section 23: Problem 4 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 if
is an infinite set, it is connected in the finite complement topology.
There are no two disjoint nonempty open subsets, as the complement of a nonempty open set is finite, and the only finite open set is the empty set.
Alternatively, closed sets are finite or
, while open sets are
or infinite.