A mathematical structure 
is said to be closed under an operation 
if, whenever 
and 
are both elements of 
,
then so is 
.
A solution to a problem that has an analytic solution in terms of standard named functions, constants, etc., is said to have a closed-form solution.
In topology, a set 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. The opposite of closed in this sense is open.
A plane curve with no endpoints and that completely encloses an area is known as a closed curve.
See also
Closed Interval, Closed-Form Solution, Closed Manifold, Closed Map, Closed Set, Open, Open Set
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Cite this as:
Weisstein, Eric W. "Closed." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Closed.html