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Difference between revisions of "Covering element"

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''in a partially ordered set''
 
''in a partially ordered set''
  
An element directly following another element; more precisely, the expression  "a covers b in the partially ordered set P"  means that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026930/c0269301.png" /> and that there is no element <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026930/c0269302.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026930/c0269303.png" />.
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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=13768
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article