The Stacks project

Definition 5.30.1. A topological group is a group $G$ endowed with a topology such that multiplication $G \times G \to G$, $(x, y) \mapsto xy$ and inverse $G \to G$, $x \mapsto x^{-1}$ are continuous. A homomorphism of topological groups is a homomorphism of groups which is continuous.

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View Definition 5.30.1 as pdf