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        "quote": "称集合 $A$ 为 $x \\in X$ 的邻域，如果存在开集 $U$ 使得 $x \\in U \\subset A$。若 $A$ 本身是开集，则称它为 $x$ 的一个 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:09ac0761-d818-449e-99c7-82395e89dbeb\" data-concept-route=\"/concept-identities#concept-09ac0761-d818-449e-99c7-82395e89dbeb\" id=\"first-bb101d48f6c982eb4018-zh\">开邻域(open neighbourhood)</u>。称拓扑空间 $X$ 为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:7c674ad2-04ad-4bb5-8434-a4c7b804b02c\" data-concept-route=\"/concept-identities#concept-7c674ad2-04ad-4bb5-8434-a4c7b804b02c\" id=\"first-b03c683ecdf83435dd9b-zh\">第一可数(first countable)</u>，如果每一点 $x \\in X$ 都有一个可数族 $U _ { 1 } ( x ) , U _ { 2 } ( x ) , \\dots$，它由 $x$ 的开邻域组成，使得 $x$ 的每个开邻域 $U$ 都包含这些邻域之一 $U \\supset U _ { n } ( x )$。一个更强的条件是：称拓扑空间 $( X , { \\mathcal { O } } )$ 为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:1ae3cb73-f44a-4483-b175-f7481d779ac8\" data-concept-route=\"/concept-identities#concept-1ae3cb73-f44a-4483-b175-f7481d779ac8\" id=\"first-d3666106efe7fd9144c7-zh\">第二可数(second countable)</u> 或可分的，如果存在一个可数集 $U _ { 1 } , U _ { 2 } , U _ { 3 } , . . .$，它生成 $X$ 的拓扑。",
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