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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}.

A map f between topological spaces that maps closed sets to closed sets. If f is bijective, then f is closed <==>f is open <==>f^(-1) is continuous, where f^(-1) denotes the ...

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closed if for any sequence of vectors v_n in D(A) such that v_n->v and Av_n->x as n->infty, it ...

A field K is said to be algebraically closed if every polynomial with coefficients in K has a root in K.

The set closure St^_v of a star Stv at a vertex v of a simplicial complex K.

A subset of a topological group which is closed as a subset and also a subgroup.

A compact manifold without boundary.