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A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

Three sets of three lines such that each line is incident with two from both other sets.

A set function mu is said to possess countable subadditivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

If F is a sigma-algebra and A is a subset of X, then A is called measurable if A is a member of F. X need not have, a priori, a topological structure. Even if it does, there ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

A set function mu possesses countable additivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

The study of definable sets and functions in polish spaces.