View source for Elementary interval

''of a partially ordered set''

A subset consisting of two elements <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035340/e0353401.png" /> such that there are no other elements in the partially ordered set between them, i.e.

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035340/e0353402.png" /></td> </tr></table>



====Comments====
Elementary intervals are also called gaps or atomic intervals.

For (elementary) intervals in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035340/e0353403.png" /> see [[Interval and segment|Interval and segment]]; [[Interval, closed|Interval, closed]]; [[Interval, open|Interval, open]].