- #1

- 94

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If [tex]X[/tex] is a finite set of [tex]n[/tex] elements, is there a way to know how many different topologies can [tex]X[/tex] have?

I think it is some combinatorial problem, but not sure.

Thanks for your help.

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- Thread starter Damidami
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- #1

- 94

- 0

If [tex]X[/tex] is a finite set of [tex]n[/tex] elements, is there a way to know how many different topologies can [tex]X[/tex] have?

I think it is some combinatorial problem, but not sure.

Thanks for your help.

- #2

- #3

- 1,631

- 4

I feel like there is a somewhat pseudo-random pattern.

- #4

- 1,631

- 4

You can find more information here.

This is so cool! It is interesting how stirling numbers show up in so many places.

However, like they say there, there doesn't seem to be an easy way of counting the number of topologies on a random set of cardinality n. Since T_0 is a well-behaved topology, it seems somewhat easier.

Does anybody know whether this is an Open Question or?

- #5

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- 0

It seems it turned to be a difficult and interesting question.

Thanks for your replys!

Thanks for your replys!

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