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The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

A set U has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that U is bounded.

A set R of linear extensions of a partially ordered set P=(X,<=) is a realizer of P (and is said to realize P) provided that for all x,y in X, x<=y iff x is below y in every ...

The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

The term annihilator is used in several different ways in various aspects of mathematics. It is most commonly used to mean the set of all functions satisfying a given set of ...

A collection B of subsets of a set X forming a topological basis.

Let P=(P,<=) be a partially ordered set, and let x,y,z in P. If x<=y<=z, then y is said to be between x and z. If y is between x and z and y not in {x,z}, then y is strictly ...

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...

The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points p_1, ..., p_N, the convex hull C is then given by the ...