Is trivial topology seperable?

Question

$(X,\mathcal T)$ is a t.s.

$\mathcal T = \{X,\emptyset\}$

How can we say space is seperable?

Answer 1

Yes trivial topology is seperable. We can say a topological space is seperable if and only if there exists at least one countable dense subset of $X$

If we consider singletons,

$\overline {\{x\}} = X$ and we know that singletons are countable thus trivial topology is seperable.

Besides any non-empty subset of $X$ is dense too

Answer 2

Any non-empty subset of $X$ is dense.