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        "quote": "> [!example] <a class=\"object-permalink\" href=\"#example-10-7\">例 10.7</a> \n>\n> 集合 $X$ 上的所有拓扑都介于两个极端之间，即离散拓扑与不可分拓扑。<u class=\"concept-term\" data-concept-identity=\"urn:uuid:99d3a8fc-4856-47a6-824e-8ee0083dec99\" data-concept-route=\"/concept-identities#concept-99d3a8fc-4856-47a6-824e-8ee0083dec99\" id=\"first-e5c6d3c4a6e37e4a4ed5-zh\">不可分拓扑(indiscrete topology)</u>（亦称平庸拓扑）仅由空集与整个空间本身 $\\mathcal { O } _ { 1 } = \\{ \\emptyset , X \\}$ 组成。它是 $X -$ 上可能的最粗拓扑：若 $\\mathcal{O}$ 是任何其他拓扑，则由 (Top1) 有 $\\mathcal { O } _ { 1 } \\subseteq \\mathcal { O }$。<u class=\"concept-term\" data-concept-identity=\"urn:uuid:0effb2c1-c32e-4d63-80be-762ba1393f3b\" data-concept-route=\"/concept-identities#concept-0effb2c1-c32e-4d63-80be-762ba1393f3b\" id=\"first-4fb6a5c1fc44932c3391-zh\">离散拓扑(discrete topology)</u> 由 $X , { \\mathcal { O } } _ { 2 } = 2 ^ { X }$ 的所有子集组成。该拓扑是 $X ,$ 上可能的最细拓扑，因为它包含所有其他拓扑 $\\mathcal { O } _ { 2 } \\supseteq \\mathcal { O }$。对于这两种拓扑，(Top1)–(Top3) 的验证都是平凡的。",
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