> 
> When is $(X, \mathcal{T}\_{trivial})$ Hausdorff?
> 
> 
> 

Recall: $\mathcal{T}\_{trivial} = \{\varnothing, X\}$

I want to say that this space is Hausdorff is $X$ is a singleton

But I can't actually produce two open sets that satisfy the condition:

> 
> $\forall x,y \in X$, there exists disjoint $U, V \in
> \mathcal{T}\_{trivial}$ such that $x \in U$ and $y \in V$
> 
> 
> 

Suppose $X = \{x\}$, then yes we have a $x \in U = \{x\}$, but do we have $y \in \varnothing$, since $\varnothing$ is empty?, or is the condition trivially satisified since there is only one point?