Namespaces
Variants
Actions

Elementary interval

From Encyclopedia of Mathematics
Revision as of 21:59, 12 October 2014 by Richard Pinch (talk | contribs) (Category:Order, lattices, ordered algebraic structures)
Jump to: navigation, search

of a partially ordered set

A subset consisting of two elements $a\leq b$ such that there are no other elements in the partially ordered set between them, i.e.

$$a\leq x\leq b\Rightarrow a=x\text{ or }a=b.$$


Comments

Elementary intervals are also called gaps or atomic intervals.

For (elementary) intervals in $\mathbf R$ see Interval and segment; Interval, closed; Interval, open.

How to Cite This Entry:
Elementary interval. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elementary_interval&oldid=33602
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article