Indiscrete Non-Singleton Space is not T0
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Then $T$ is not a $T_0$ (Kolmogorov) space.
Let $a, b \in S$.
So (trivially) there is no open set in $T$ containing $a$ and not $b$, or $b$ and not $a$.
Hence the result, by definition of $T_0$ (Kolmogorov) space.