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An algebraic set is the locus of zeros of a collection of polynomials. For example, the circle is the set of zeros of x^2+y^2-1 and the point at (0,0) is the set of zeros of ...

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 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 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 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.

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

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.

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

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

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