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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 ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

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 ...

If A and B are commutative unit rings, and A is a subring of B, then A is called integrally closed in B if every element of B which is integral over A belongs to A; in other ...

A discrete function A(n,k) is called closed form (or sometimes "hypergeometric") in two variables if the ratios A(n+1,k)/A(n,k) and A(n,k+1)/A(n,k) are both rational ...

A mathematical object S is said to be additively closed if a,b in S implies that a+b in S.

A mathematical object S is said to be multiplicatively closed if a,b in S implies that ab in S.

In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

An n-dimensional closed disk of radius r is the collection of points of distance <=r from a fixed point in n-dimensional Euclidean space. Krantz (1999, p. 3) uses the symbol ...

The closed ball with center x and radius r is defined by B_r(x)={y:|y-x|<=r}.