I find it difficult to understand one of the properties and the definition of Hausdorff spaces.
The property states that, "If $X$ is Hausdorff then every finite set is closed. How is this possible keeping in mind that the definition states that for two distinct elements you can find an open neighborhood around them such that their intersection is empty. Thus, wouldn't the finite set be open because you can always find an open neighborhood around distinct elements of finite sets?
Can someone please explain?