Lemma 40.1.14.label Let $G$ be an infinite group and $G \curvearrowright X$ be minimal $G$-flow, then every point in $X$ is recurrent.
Proof. Let $x \in X$ and $U \in \cn_{X}(x)$, then $N(x, U)$ is syndetic. As $G$ is infinite, so is $N(x, U)$.$\square$
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