Can someone please help me with this problem?
Assume that $(X, T)$ is a topological space and that $B$ is a basis for the topology $T$. Show that $(X, T)$ is $T_2$ if and only if for all $x$ and $y$ in $X$, there are elements $B_1$ and $B_2$ of $B$, such that $B_1 \cap B_2 = \varnothing$, $x \in B_1$, and $y \in B_2$.
thanks