Elementary interval

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of a partially ordered set

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


Elementary intervals are also called gaps or atomic intervals.

For (elementary) intervals in see Interval and segment; Interval, closed; Interval, open.

How to Cite This Entry:
Elementary interval. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article