Definition 4.3.4 (Convergence). Let $X$ be a topological space and $\net{x}\subset X$, then $\net{x}$ converges to $x$ if for every $U \in \cn(x)$, $\net{x}$ is eventually in $U$, denoted $x_{\alpha} \to x$.
Definition 4.3.4 (Convergence). Let $X$ be a topological space and $\net{x}\subset X$, then $\net{x}$ converges to $x$ if for every $U \in \cn(x)$, $\net{x}$ is eventually in $U$, denoted $x_{\alpha} \to x$.