Resolvable space explained

In topology, a topological space is said to be resolvable if it is expressible as the union of two disjoint dense subsets. For instance, the real numbers form a resolvable topological space because the rationals and irrationals are disjoint dense subsets. A topological space that is not resolvable is termed irresolvable.

Properties

• The product of two resolvable spaces is resolvable
• Every locally compact topological space without isolated points is resolvable
• Every submaximal space is irresolvable

See also

• Glossary of topology