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I would like to know if there is like a magical formula to know how many topologies exist on a finite set

For example for $X = \{ a, b, c \}$ I found $29$, but I dont know if there are more or how to know this exact number without writing all topologies first.

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See oeis.org/A000798 and the references therein. –  Robert Israel Feb 17 '13 at 20:37
This link maybe helpful for you: jstor.org/stable/2313548 –  Anirban Oct 24 '14 at 12:40

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