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Yes. Better, it works for T1$T_1$, too: T1$T_1$ is the axiom that one-point sets are closed.
Then since the set is finite, the complement of any point is also closed; the point is open. That's the discrete topology.
Yes. Better, it works for T1, too: T1 is the axiom that one-point sets are closed.
Yes. Better, it works for $T_1$, too: $T_1$ is the axiom that one-point sets are closed.
