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.
Propertiesedit
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
A.Illanes (1996), "Finite and \omega-resolvability", Proc. Amer. Math. Soc., 124: 1243–1246, doi:10.1090/s0002-9939-96-03348-5
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resolvable, space, topology, topological, space, said, resolvable, expressible, union, disjoint, dense, subsets, instance, real, numbers, form, resolvable, topological, space, because, rationals, irrationals, disjoint, dense, subsets, topological, space, that,. 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 editThe product of two resolvable spaces is resolvable Every locally compact topological space without isolated points is resolvable Every submaximal space is irresolvableSee also editGlossary of topologyReferences editA B Kharazishvili 2006 Strange functions in real analysis Chapman amp Hall CRC monographs and surveys in pure and applied mathematics vol 272 CRC Press p 74 ISBN 1 58488 582 3 Miroslav Husek 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 doi 10 1090 s0002 9939 96 03348 5 nbsp This topology related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Resolvable space amp oldid 1204831633, wikipedia, wiki, book, books, library,
