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        "quote": "> [!example] <a class=\"object-permalink\" href=\"#example-10-13\">例 10.13</a> \n>\n> 设 $S ^ { 1 }$ 为 $\\mathbb { R } ^ { 2 }$ 中由 $x ^ { 2 } + y ^ { 2 } = 1$ 定义的单位圆，并赋予相对拓扑。乘积空间 $S ^ { 1 } \\times S ^ { 1 }$ 同胚于 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:fee87ca7-4cd9-4a1f-ab6b-9f29f4e871d4\" data-concept-route=\"/concept-identities#concept-fee87ca7-4cd9-4a1f-ab6b-9f29f4e871d4\" id=\"first-e32baf3c671c03264106-zh\">环面(torus)</u> $T ^ { 2 }$，或称“甜甜圈”，其拓扑由它作为 $\\mathbb { R } ^ { 3 }$ 的子集的嵌入诱导得到。这可以通过将 $S ^ { 1 }$ 嵌入 $\\mathbb { R } ^ { 3 }$ 的 $z = 0$ 平面，并在 $S ^ { 1 }$ 上的每一点处附着一个朝外的竖直单位圆来看出。当这些竖直圆沿水平圆“扫过”时，所得出的圆显然是一个环面。",
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