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In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.

The index set for the collection of submodules in a graded module.

The continuous image of a Polish space, also called an analytic set.

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...

A totally ordered set (A,<=) is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element (Ciesielski 1997, p. 38; Moore 1982, ...

A set function is a function whose domain is a collection of sets. In many instances in real analysis, a set function is a function which associates an affinely extended real ...

A set S is discrete in a larger topological space X if every point x in S has a neighborhood U such that S intersection U={x}. The points of S are then said to be isolated ...

A partially ordered set is defined as an ordered pair P=(X,<=). Here, X is called the ground set of P and <= is the partial order of P.

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...