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Separable space
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==Constructive mathematics== Separability is especially important in [[numerical analysis]] and [[Mathematical constructivism|constructive mathematics]], since many theorems that can be proved for nonseparable spaces have constructive proofs only for separable spaces. Such constructive proofs can be turned into [[algorithm]]s for use in numerical analysis, and they are the only sorts of proofs acceptable in constructive analysis. A famous example of a theorem of this sort is the [[Hahn–Banach theorem]].
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