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A set of plane measure 0 that contains a circle of every radius.

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 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 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 ...

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 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.

A set S together with a relation >= which is both transitive and reflexive such that for any two elements a,b in S, there exists another element c in S with c>=a and c>=b. In ...