# Topology Question

• January 7th 2009, 04:00 PM
flaming
Topology Question
Question 1

(a) Give an example of a space where the discrete topology is the same as the finite complement topology.
• January 7th 2009, 07:25 PM
ThePerfectHacker
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 $X$ be a finite set. Then the discrete topology is simply $\mathcal{P}(X)$. But since $X$ is finite it means the complement of any $Y\subseteq X$ is finite. Thus, the finite complement topology consists of all subsets of $X$ i.e. $\mathcal{P}(X)$.