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A334254 Number of closure operators on a set of n elements which satisfy the T_1 separation axiom. 2
1, 2, 1, 8, 545, 702525 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The T_1 axiom states that all singleton sets {x} are closed.

For n>1, this property implies strictness (meaning that the empty set is closed).

LINKS

Table of n, a(n) for n=0..5.

Eric Weisstein's World of Mathematics, Separation Axioms

Wikipedia, Separation Axiom

EXAMPLE

The a(3) = 8 set-systems of closed sets:

{{1,2,3},{1},{2},{3},{}}

{{1,2,3},{1,2},{1},{2},{3},{}}

{{1,2,3},{1,3},{1},{2},{3},{}}

{{1,2,3},{2,3},{1},{2},{3},{}}

{{1,2,3},{1,2},{1,3},{1},{2},{3},{}}

{{1,2,3},{1,2},{2,3},{1},{2},{3},{}}

{{1,2,3},{1,3},{2,3},{1},{2},{3},{}}

{{1,2,3},{1,2},{1,3},{2,3},{1},{2},{3},{}}

CROSSREFS

The number of all closure operators is given in A102896.

For T_0 closure operators, see A334252.

For strict T_1 closure operators, see A334255, the only difference is a(1).

Cf. A326960, A326961, A326979.

Sequence in context: A224090 A013327 A009349 * A230582 A011186 A078088

Adjacent sequences:  A334251 A334252 A334253 * A334255 A334256 A334257

KEYWORD

nonn,more

AUTHOR

Joshua Moerman, Apr 20 2020

STATUS

approved

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Last modified December 4 21:14 EST 2020. Contains 338938 sequences. (Running on oeis4.)