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Difference between revisions of "Nerve of a family of sets"

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The [[Simplicial complex|simplicial complex]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066310/n0663102.png" /> with as simplices the finite non-empty subsets of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066310/n0663103.png" /> with non-empty intersection. In particular, the vertices of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066310/n0663104.png" /> are the non-empty elements of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066310/n0663105.png" />.
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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 $\alpha$.

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=31623
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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