# Covering element

From Encyclopedia of Mathematics

*in a partially ordered set*

An element directly following another element; more precisely, the expression "$b$ covers $a$ in the partially ordered set $(P,{<})$" means that $a < b$ and that there is no element $x\in P$ such that $a<x<b$: the interval $[a,b]$ is an *atomic* or *elementary interval*.

**How to Cite This Entry:**

Covering element.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Covering_element&oldid=37625

This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article