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
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,
ISBN1-58488-582-3
Miroslav Hušek; J. van Mill (2002), Recent progress in general topology, Recent Progress in General Topology, vol. 2, Elsevier, p. 21,
ISBN0-444-50980-1