$T_1$- ness of a topological space

Question

Basis of odd even topology like $\{\{1,2\},\{2,3\},.....\}$. I think $\{1,2\}$ and $\{2,3\}$ are different open set here. Then why odd even topology is not $T_1$? please explain

Answer 1

Its not even $T_0$: every open set that contains $0$ also contains $1$ and vice versa. Likewise for all pairs $2k-1,2k$