Covering element

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