partial updates for review, and fix typos
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## Convergence of sequences
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Let $X$ be a topological space and $\{x_n\}_{n\in\mathbb{N}_+}$ be a sequence of points in $X$. WE say $x_n\to x$ as $n\to \infty$ ($x_n$ converges to $x$ as $n\to \infty$)
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Let $(X,\mathcal{T})$ be a topological space and $\{x_n\}_{n\in\mathbb{N}_+}$ be a sequence of points in $X$. We say $x_n\to x$ as $n\to \infty$ ($x_n$ converges to $x$ as $n\to \infty$)
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if for any open neighborhood $U$ of $x$, there exists $N\in\mathbb{N}_+$ such that $\forall n\geq N, x_n\in U$.
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