Resolvable space
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
- 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 HuĊĦek; J. van Mill (2002), Recent progress in general topology, Recent Progress in General Topology 2, Elsevier, p. 21, ISBN 0-444-50980-1
This article is issued from Wikipedia - version of the Monday, May 07, 2012. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.