The Stacks project

Definition 5.30.7. A topological ring is a ring $R$ endowed with a topology such that addition $R \times R \to R$, $(x, y) \mapsto x + y$ and multiplication $R \times R \to R$, $(x, y) \mapsto xy$ are continuous. A homomorphism of topological rings is a homomorphism of rings which is continuous.

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