Viewing topic: Open Interval

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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 {x|a < 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