A mathematical structure A is said to be closed under an operation + if, whenever a and b are both elements of A, then so is a+b.

A mathematical object taken together with its boundary is also called closed. For example, while the interior of a sphere is an open ball, the interior together with the sphere itself is a closed ball.

See also

Closed Ball, Closed Curve, Closed Curve Problem, Closed Disk, Closed Form, Closed-Form Solution, Closed Manifold, Closed Map, Closed Sentential Formula, Closed Set, Closed Star, Closed Subgroup, Closure, Topological Closure

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Cite this as:

Weisstein, Eric W. "Closed." From MathWorld--A Wolfram Web Resource.

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