Definition 6.6.4 (Cauchy Net).label Let $(X, \fU)$ be a uniform space and $\net{x}\subset X$ be a net, then $\net{x}$ is Cauchy if for any $V \in \fU$, there exists $\alpha_{0} \in A$ such that $(x_{\alpha}, x_{\beta}) \in V$ for all $\alpha, \beta \ge \alpha_{0}$.