Definition 85.4.11. Let $\varphi : A \to B$ be a continuous map of linearly topologized rings. We say $\varphi $ is *taut*^{1} if for every open ideal $I \subset A$ the closure of the ideal $\varphi (I)B$ is open and these closures form a fundamental system of open ideals.

[1] This is nonstandard notation. The definition generalizes to modules, by saying a linearly topologized $A$-module $M$ is $A$-taut if for every open ideal $I \subset A$ the closure of $IM$ in $M$ is open and these closures form a fundamental system of neighbourhoods of $0$ in $M$.

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