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        "quote": "给定拓扑空间 $S ,$ 的一个开覆盖 $\\{ U _ { i } | i \\in I \\}$，若对于每个 $i \\in I$ 都有 $V _ { a } \\subseteq U _ { i }$，则称 $S$ 的开覆盖 $\\{ V _ { a } \\}$ 为 $\\{ U _ { i } \\}$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:defda17a-18a4-441f-bd21-63aeaa375b3f\" data-concept-route=\"/concept-identities#concept-defda17a-18a4-441f-bd21-63aeaa375b3f\" id=\"first-d9fa818df9de9f675c8b-zh\">加细(refinement)</u>。若每一点 $p$ 至多属于有限个 $V _ { a } \\mathbf { \\bar { s } } .$，则称该加细是 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:b32fccab-0ef7-4fc4-bec9-9aee534e4afc\" data-concept-route=\"/concept-identities#concept-b32fccab-0ef7-4fc4-bec9-9aee534e4afc\" id=\"first-cfb8584a54bc36367766-zh\">局部有限的(locally finite)</u>。若对每个开覆盖 $U _ { i } \\left( i \\in I \\right)$ 都存在局部有限的加细，则称拓扑空间 $S$ 是 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:9a348175-31ec-4401-afa6-cb89bf54511c\" data-concept-route=\"/concept-identities#concept-9a348175-31ec-4401-afa6-cb89bf54511c\" id=\"first-e0b213c4c786619739d5-zh\">仿紧的(paracompact)</u>。由于可以证明每个局部紧 Hausdorff 第二可数空间都是仿紧的 [12]，因此从现在起我们将注意力限制在作为仿紧拓扑空间的流形上。",
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