Abstract
Let H be an integral domain, and let Σ be a collection of integrally closed overrings of H. We show that if A is an overring of H such that , and if Σ is a Noetherian subspace of the space of all integrally closed overrings of H, then there exists a weakly Noetherian subspace Γ of integrally closed overrings of H such that , and no member of Γ can be omitted from this intersection. Restricting to the case where Σ consists of valuation overrings, we obtain stronger results.
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