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# Resolvable space

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

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 HuĊĦek; J. van Mill (2002), Recent progress in general topology, Recent Progress in General Topology 2, Elsevier, p. 21, ISBN 0-444-50980-1

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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