Nerve of a family of sets
The simplicial complex $K(\alpha)$ with as simplices the finite non-empty subsets of $\alpha$ with non-empty intersection. In particular, the vertices of $K(\alpha)$ are the non-empty elements of $\alpha$.
Nerve of a family of sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Nerve_of_a_family_of_sets&oldid=31624