Give an example of a topological space that is separable but not a Hausdorff space.
I have not been able to discover an example, I thought of the Arens-Fort space because this is separable, since this space is countable and the same set is a countable dense about yourself, but do not know how to show that is second-countable. This space serves as an example, there are some other more. Thanks
Best Answer
Just take a finite space that isn't Hausdorff, such as the set $X=\{s,\eta\}$ with the topology where the open sets are $X$, $\emptyset$, and $\{\eta\}$.