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co.combinatorics - Number of metric spaces on N points - MathOverflow
https://mathoverflow.net/questions/1677/number-of-metric-spaces-on-n-points
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Given $X = \{x_1, ..., x_n\}$, how many collections $C$ of subsets of $X$ are there such that $C$ is the listing of all open balls of some metric space? The first nontrivial example is $n=3$; let's...
