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A generalization of the concept of set unions and intersections.

Fatou dust is a Fatou set for a point outside the underlying set. Such a set has zero area and has an infinite number of disconnected components.

A set of four, also called a tetrad.

X subset= R^n is subanalytic if, for all x in R^n, there is an open set U and a bounded semianalytic set Y subset R^(n+m) such that X intersection U is the projection of Y ...

A relation R on a set S is reflexive provided that xRx for every x in S.

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

The ideal generated by a set in a vector space.

A set equipped with a sigma-algebra of subsets.

For every partition of all the points on a line into two nonempty sets such that no point of either lies between two points of the other, there is a point of one set which ...

A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.