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|Paper IPM / M / 8559||
In this note, we show that a compact Hausdorff space X is dense-separable if and only if every family of ideals of C(X) with zero intersection has a countable subfamily with zero intersection. As a consequence of this characterization we observe that every compact dense-separable space with Soc(C(X))=0 has a countable dense and co-dense subset.
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