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Interval

Definition: Suppose that X is a set having a simple order relation <. Given element a and b of X such that a<b, there are four subsets of X that are called the intervals determined by a and b. They are the following: (a, b)={xa < x < b}, (a, b]={xa < x<= b}, [a, b)={xa <= x < b}, [a, b]={a <= x <= b}. A set of the first type is called an open interval in X, a set of the last type is called a closed interval in X, and sets of the second and third types are called halfopen intervals.
Source: Topology (second edition) by James R. Munkres
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