Topology Question

Question 1

(a) Give an example of a space where the discrete topology is the same as the finite complement topology.

Quote:

---

Originally Posted by flaming

Question 1

(a) Give an example of a space where the discrete topology is the same as the finite complement topology.

---

Let be a finite set. Then the discrete topology is simply . But since is finite it means the complement of any is finite. Thus, the finite complement topology consists of all subsets of i.e. .