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

## References

- A.B. Kharazishvili (2006),
*Strange functions in real analysis*, Chapman & Hall/CRC monographs and surveys in pure and applied mathematics,**272**, CRC Press, p. 74, ISBN 1-58488-582-3 - Miroslav Hušek; J. van Mill (2002),
*Recent progress in general topology*, Recent Progress in General Topology,**2**, Elsevier, p. 21, ISBN 0-444-50980-1 - A.Illanes (1996), "Finite and \omega-resolvability",
*Proc. Amer. Math. Soc.*,**124**: 1243–1246, doi:10.1090/s0002-9939-96-03348-5