Lemma 87.5.4 (0GX3)—The Stacks project

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Table of contents
Part 5: Topics in Geometry
Chapter 87: Formal Algebraic Spaces
Section 87.5: Taut ring maps
Lemma 87.5.4 (cite)

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Lemma 87.5.4. Let $A \to B$ and $B \to C$ be continuous homomorphisms of linearly topologized rings. If $A \to B$ and $B \to C$ are taut, then $A \to C$ is taut.

Proof. Omitted. Hint: if $I \subset A$ is an ideal and $J$ is the closure of $IB$ , then the closure of $JC$ is equal to the closure of $IC$ . $\square$

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