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A set whose members index (label) members of another set. For example, in the set A= union _(k in K)A_k, the set K is an index set of the set A.

A definable set, also called a Souslin set.

Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...

A set S of integers is said to be recursive if there is a total recursive function f(x) such that f(x)=1 for x in S and f(x)=0 for x not in S. Any recursive set is also ...

A hom-set of a category C is a set of morphisms of C.

A theorem about (or providing an equivalent definition of) compact sets, originally due to Georg Cantor. Given a decreasing sequence of bounded nonempty closed sets C_1 ...

The limit points of a set P, denoted P^'.

An analytic, Borel, or coanalytic set.

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...

An orthonormal set is a set of normalized orthogonal vectors or functions.