Possible Duplicate:
Checking separation axiom
Let $R$ be an topology on $\mathbb{R}$ defined by $V$ open if and only if either $0\in V$ or $2\notin V$. Would you help me how to check whether $R$ satisfiying separation axiom $T_1$ .
My work: Let $V$ be open set containing $2$. By definition, $0\in V$. Note that $0\neq 2$. Since for all $V$ open that containing $2$, we have $0\in V$ then $T_1$ is not satisfied. Thanks.