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Open Interval

Definition: If X is a set and , is an order relation on X, and if a<b, we use the notation (a, b) to denote the set {xa < x < b}; it is called an open interval in X. If this set is empty, we call a the immediate predecessor of b, and we call b the immediate successor of a.
Source: Topology (second edition) by James R. Munkres
10:02pm 9/21/2015
User: HenryMiller
Post count: 10
The terms "Open" and "Closed" are sometimes used when the end value is included or not: (a, b) a < x < b an open interval [a, b) a ≤ x < b closed on left, open on right (a, b] a < x ≤ b open on left, closed on right [a, b] a ≤ x ≤ b a closed interval