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If S is an infinite set, then the collection F_S={A subset= S:S-A is finite} is a filter called the cofinite (or Fréchet) filter on S.

The homeomorphism group of a topological space X is the set of all homeomorphisms f:X->X, which forms a group by composition.

A tree having an infinite number of branches and whose nodes are sequences generated by a set of rules.

The Zermelo-Fraenkel axioms are the basis for Zermelo-Fraenkel set theory. In the following (Jech 1997, p. 1), exists stands for exists, forall means for all, in stands for ...

The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.

The function from a given nonempty set X to the power set P(X) that maps every element x of X to the set {x}.

The set of points, known as boundary points, which are members of the set closure of a given set S and the set closure of its complement set. The boundary is sometimes called ...

Let S be a nonempty set, then a filter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F, 2. If A,B in F, then A ...

A superset which is not the entire set.

Every bounded infinite set in R^n has an accumulation point. For n=1, an infinite subset of a closed bounded set S has an accumulation point in S. For instance, given a ...