# Similarity and Difference between Separable Space and Separated space?

Does separability and/or second countability implies $$T_2$$ or higher axiom sets?

My intuition is "no". Even $$T_0$$ space can be separability and/or second countability?

No. Consider $$X = \{a,b\}$$ just two elements and $$\mathcal{T} = \{\emptyset, X\}$$. This is separable, second countable, and not even $$T_0$$.