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        "quote": "称点 $x$ 为集合 $A$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:219d9a3a-91e9-494e-a7b3-9e7b8ac0a94a\" data-concept-route=\"/concept-identities#concept-219d9a3a-91e9-494e-a7b3-9e7b8ac0a94a\" id=\"first-ee256cff758d65df9a43-zh\">聚点(accumulation point)</u>，如果 $x$ 的每个开邻域 $U$ 都含有 $A$ 中异于 $x$ 本身的点，如图 10.3 所示。这意味着 $x$ 可能属于也可能不属于 $A$，但 $A$ 的点可以任意接近它而“聚集”在其附近（有时也称它为 $A$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:cb88c09e-14e0-4771-bcbb-e14fb4570805\" data-concept-route=\"/concept-identities#concept-cb88c09e-14e0-4771-bcbb-e14fb4570805\" id=\"first-7138e5c13fd391712893-zh\">聚点(cluster point)</u>）。$A$ 相关概念通常应用于点序列 $x _ { n } \\in X$。若对 $x$ 的每个开邻域 $U$，都存在整数 $N$，使得对所有 $n \\geq N$ 都有 $x _ { n } \\in U$，则称序列 $x _ { n } \\in X$ 收敛到 $x \\in X$，或称 $x$ 是 $\\{ x _ { n } \\}$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:0009d7dc-5f4f-4928-a8cc-fa12def8161c\" data-concept-route=\"/concept-identities#concept-0009d7dc-5f4f-4928-a8cc-fa12def8161c\" id=\"first-3f83681b3847dbd4e0e1-zh\">极限点(limit point)</u>，记作 $x _ { n } \\to x ,$。这与聚点的区别在于，对某个 $n _ { 0 }$，可能对所有 $n > n _ { 0 }$ 都有 $x _ { n } = x$",
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