Difference between revisions of "Nerve of a family of sets"
From Encyclopedia of Mathematics
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| − | The [[Simplicial complex|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 $\alpha$. | + | The [[Simplicial complex|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 $\alpha$. |
Latest revision as of 12:24, 12 April 2014
$\alpha$
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://encyclopediaofmath.org/index.php?title=Nerve_of_a_family_of_sets&oldid=31624
Nerve of a family of sets. Encyclopedia of Mathematics. URL: http://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