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        "quote": "称集合族 $\\mathcal { U } = \\{ U _ { i } \\vert i \\in I \\}$ 为拓扑空间 $X$ 的子集 $A$ 的一个 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:77d78323-eba1-47e1-ada3-16aa434adb16\" data-concept-route=\"/concept-identities#concept-77d78323-eba1-47e1-ada3-16aa434adb16\" id=\"first-84ecf433fadcf1b3b273-zh\">覆盖(covering)</u>，如果每一点 $x \\in A$ 都属于该集合族中的某个成员。若其中每个成员都是开集，则称之为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:52e98d74-140a-45ae-9670-fcdb38942d97\" data-concept-route=\"/concept-identities#concept-52e98d74-140a-45ae-9670-fcdb38942d97\" id=\"first-96a4c3059f1e03dc322d-zh\">开覆盖(open covering)</u>。该覆盖的一个子集 $\\mathcal{U}^\\prime \\subseteq \\mathcal{U}$ 若覆盖 $A$，则称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:40652117-ec64-4eda-8fa8-bdfb858b1aa2\" data-concept-route=\"/concept-identities#concept-40652117-ec64-4eda-8fa8-bdfb858b1aa2\" id=\"first-76c097697b1f74e8b7ad-zh\">子覆盖(subcovering)</u>。若 $\\mathcal{U}^\\prime$ 由有限多个集合 $\\left\\{ U _ { 1 } , U _ { 2 } , \\dots , U _ { n } \\right\\}$ 组成，则称之为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:9cd293e5-41f8-41f6-bc80-04d11b5fe31b\" data-concept-route=\"/concept-identities#concept-9cd293e5-41f8-41f6-bc80-04d11b5fe31b\" id=\"first-b1489a82892540b65f5f-zh\">有限子覆盖(finite subcovering)</u>。",
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