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
References
References
- A.B. Kharazishvili (2006), Strange functions in real analysis, Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, vol. 272, CRC Press, p. 74, ISBN 1-58488-582-3
- Miroslav Hušek; J. van Mill (2002), Recent progress in general topology, vol. 2, Elsevier, p. 21, ISBN 0-444-50980-1
- A.Illanes (1996), "Finite and \omega-resolvability", Proc. Amer. Math. Soc., 124 (4): 1243–1246, doi:10.1090/s0002-9939-96-03348-5