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A set which contains a nonnegative integral number of elements is said to be finite. A set which is not finite is said to be infinite. A finite or countably infinite set is ...

An infinite set, such as the real numbers, which is not countably infinite.

A subset is a portion of a set. B is a subset of A (written B subset= A) iff every member of B is a member of A. If B is a proper subset of A (i.e., a subset other than the ...

A distance graph with distance set (0,1].

A mathematical object (such as a set or function) is said to bounded if it possesses a bound, i.e., a value which all members of the set, functions, etc., are less than.

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 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.