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 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
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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