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Closed Interval

ClosedInterval

A closed interval is an interval that includes all of its limit points. If the endpoints of the interval are finite numbers a and b, then the interval {x:a<=x<=b} is denoted [a,b]. If one of the endpoints is +/-infty, then the interval still contains all of its limit points (although not all of its endpoints), so [a,infty) and (-infty,b] are also closed intervals, as is the interval (-infty,infty).

See also

Closed Ball, Closed Disk, Closed Set, Half-Closed Interval, Interval, Limit Point, Open Interval

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References

Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 1, 1991.Gemignani, M. C. Elementary Topology. New York: Dover, 1990.

Referenced on Wolfram|Alpha

Closed Interval

Cite this as:

Weisstein, Eric W. "Closed Interval." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ClosedInterval.html

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