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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.

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 ...

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

A nonempty set is a set containing one or more elements. Any set other than the empty set emptyset is therefore a nonempty set. Nonempty sets are sometimes also called ...

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

An analytic, Borel, or coanalytic set.

A (symmetrical) boundary set of radius r and center x_0 is the set of all points x such that |x-x_0|=r. Let x_0 be the origin. In R^1, the boundary set is then the pair of ...

A set fixed within the framework of a theory and consisting of all objects considered in this theory. The complement of the universal set is the empty set.

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...