Resolvable space
In
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 pointsis resolvable
- Every submaximal spaceis irresolvable
See also
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, 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: 1243–1246,
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