Resolvable space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

History

Origin

The term resolvable space was introduced by E. Hewitt in 1943.

Definition

Symbol-free definition

A topological space is said to be resolvable if it has two disjoint dense subsets. Note that since any subset containing a dense subset is dense, this is equivalent to saying that it is expressible as a union of two disjoint dense subsets.

Examples

The real numbers form a resolvable space. The rationals and irrationals both form disjoint dense subsets.

Relation with other properties

Weaker properties

• Almost resolvable space

References

• A problem of set-theoretic topology by E. Hewitt, Duke Math J., 1943