Inequivalent Topologies Up to Cardinality 11

Comprehensive lists of inequivalent (nonhomeomorphic) topologies on n points for 2 ≤ n ≤ 11 can be found below in two different formats. Each format presents a space-delimited list of closures {x} (alternatively each line can be interpreted as a minimal base) where X = {0,...,n−1} and bit strings represent sets in the usual way where the kth bit is 1 iff k is an element of the set. One format presents bit strings explicitly and the other lists them in decimal format assuming the bit strings are big-endian. Cardinality 11 is only available in decimal format due to file size. Each zip file contains cardinalities 2 through 9.

Special thanks to Brendan McKay for kindly providing me with all inequivalent topologies on 2 through 9 points and software to compute them myself for arbitrarily large cardinalities. The algorithm is summarized in Brinkmann and McKay's paper Counting Unlabelled Topologies and Transitive Relations.

Mark Bowron
August 2021

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binary.zip (5.2 MB)
decimal.zip (3.4 MB)

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11-spaces_all_79501654_decimal.txt.gz (390 MB)
11-spaces_non-T_0_decimal.txt.gz (173 MB)
11-spaces_T_0_decimal.txt.gz (217 MB)
10-spaces_all_4717687.txt.gz (29 MB)
10-spaces_all_decimal.txt.gz (22 MB)
10-spaces_non-T_0_2150403.txt.gz (14 MB)
10-spaces_non-T_0_decimal.txt.gz (11 MB)
10-spaces_T_0_2567284.txt.gz (15 MB)
10-spaces_T_0_decimal.txt.gz (11 MB)
9-spaces_all_363083.txt.gz (2.8 MB)
9-spaces_all_decimal.txt.gz (1.7 MB)
9-spaces_T_0_183231.txt.gz (0.6 MB)
9-spaces_T_0_decimal.txt.gz (0.5 MB)
9-spaces_non-T_0_179852.txt.gz (1.4 MB)
9-spaces_non-T_0_decimal.txt.gz (0.9 MB)
8-spaces_all_35979.txt
8-spaces_all_decimal.txt
8-spaces_T_0_16999.txt
8-spaces_T_0_decimal.txt
8-spaces_non-T_0_18980.txt
8-spaces_non-T_0_decimal.txt
7-spaces_all_4535.txt
7-spaces_all_decimal.txt
7-spaces_T_0_2045.txt
7-spaces_T_0_decimal.txt
7-spaces_non-T_0_2490.txt
7-spaces_non-T_0_decimal.txt
6-spaces_all_718.txt
6-spaces_all_decimal.txt
6-spaces_T_0_318.txt
6-spaces_T_0_decimal.txt
6-spaces_non-T_0_400.txt
6-spaces_non-T_0_decimal.txt
5-spaces_all_139.txt
5-spaces_all_decimal.txt
5-spaces_T_0_63.txt
5-spaces_T_0_decimal.txt
5-spaces_non-T_0_76.txt
5-spaces_non-T_0_decimal.txt
4-spaces_all_33.txt
4-spaces_all_decimal.txt
4-spaces_T_0_16.txt
4-spaces_T_0_decimal.txt
4-spaces_non-T_0_17.txt
4-spaces_non-T_0_decimal.txt
3-spaces_all_9.txt
3-spaces_all_decimal.txt
3-spaces_T_0_5.txt
3-spaces_T_0_decimal.txt
3-spaces_non-T_0_4.txt
3-spaces_non-T_0_decimal.txt
2-spaces_all_3.txt
2-spaces_all_decimal.txt
2-spaces_T_0_2.txt
2-spaces_T_0_decimal.txt
2-spaces_non-T_0_1.txt
2-spaces_non-T_0_decimal.txt

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