Resolvable space
{{Short description|Concept in topology}}
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
References
- {{citation | title=Strange functions in real analysis | volume=272 | series=Chapman & Hall/CRC monographs and surveys in pure and applied mathematics | author=A.B. Kharazishvili | publisher=CRC Press | year=2006 | isbn=1-58488-582-3 | page=74 }}
- {{citation | title=Recent progress in general topology | volume=2 | series=Recent Progress in General Topology | author1=Miroslav Hušek | author2=J. van Mill | publisher=Elsevier | year=2002 | isbn=0-444-50980-1 | page=21 }}
- {{citation | title=Finite and \omega-resolvability | volume=124 | journal=Proc. Amer. Math. Soc. | author=A.Illanes | year=1996| pages=1243–1246 | doi=10.1090/s0002-9939-96-03348-5| doi-access=free }}
Category:Properties of topological spaces
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