Difference between revisions of "Covering element"
From Encyclopedia of Mathematics
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| − | An element directly following another element; more precisely, the expression "a | + | 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 and segment|interval]] $[a,b]$ is an ''atomic'' or ''[[elementary interval]]''. |
Latest revision as of 07:37, 24 January 2016
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
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