Definition 53.2.1. Let $G$ be a topological group. A $G$-set, sometime called a discrete $G$-set, is a set $X$ endowed with a left action $a : G \times X \to X$ such that $a$ is continuous when $X$ is given the discrete topology and $G \times X$ the product topology. A morphism of $G$-sets $f : X \to Y$ is simply any $G$-equivariant map from $X$ to $Y$. The category of $G$-sets is denoted $G\textit{-Sets}$.

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