# Nerve of a family of sets

From Encyclopedia of Mathematics

*$\alpha$*

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 $\alpha$.

**How to Cite This Entry:**

Nerve of a family of sets.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Nerve_of_a_family_of_sets&oldid=31624

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article