Separation axiom

Let $(X, \tau)$ - a topological-space.

1. First: $\forall x,y \in X:,\exists U(x), V(y) \in \tau \hookrightarrow x \not\in V(y),,,y \not\in U(x)$
2. Second (Hausdorff): $\forall x,y \in X:,\exists U(x), V(y) \in \tau \hookrightarrow U(x) \cap V(y) = \varnothing$