Interval, open

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open segment

The set of points contained in between two given constants and , i.e. satisfying the condition . An open interval does not contain the end points, and is denoted by , as distinct from the (closed) segment (a closed interval), which contains the end points, i.e. consists of the points , .


See also Interval, closed; Interval and segment.

Many authors use the (increasingly popular) alternative to denote the open interval .

How to Cite This Entry:
Interval, open. Encyclopedia of Mathematics. URL:,_open&oldid=15890
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article