Resolvable space: Difference between revisions
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==History== | |||
===Origin=== | |||
{{term introduced by|Hewitt}} | |||
The term '''resolvable space''' was introduced by E. Hewitt in 1943. | |||
==Definition== | ==Definition== | ||
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* [[Almost resolvable space]] | * [[Almost resolvable space]] | ||
==References== | |||
* ''A problem of set-theoretic topology'' by E. Hewitt, ''Duke Math J., 1943'' | |||
Revision as of 12:39, 18 August 2007
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
History
Origin
The term resolvable space was introduced by E. Hewitt in 1943.
Definition
Symbol-free definition
A topological space is said to be resolvable if it has two disjoint dense subsets. Note that since any subset containing a dense subset is dense, this is equivalent to saying that it is expressible as a union of two disjoint dense subsets.
Examples
The real numbers form a resolvable space. The rationals and irrationals both form disjoint dense subsets.
Relation with other properties
Weaker properties
References
- A problem of set-theoretic topology by E. Hewitt, Duke Math J., 1943