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        "quote": "一个微分 $r$-形式 $\\alpha$ 若满足 $\\mathrm{d}\\alpha=0$，则称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:4f8194d3-f4b1-47a6-8101-aa8cd016f6e1\" data-concept-route=\"/concept-identities#concept-4f8194d3-f4b1-47a6-8101-aa8cd016f6e1\" id=\"first-0bbe12462b1c9456320e-zh\">闭形式(closed form)</u>；若存在一个 $(r-1)$-形式 $\\beta$ 使得 $\\alpha = \\mathrm { d } \\beta$，则称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:c7b763c7-2046-4023-85d1-954aaaf12c0d\" data-concept-route=\"/concept-identities#concept-c7b763c7-2046-4023-85d1-954aaaf12c0d\" id=\"first-21de2db070b1774c8490-zh\">恰当形式(exact form)</u>。显然，每个恰当 $r$-形式都是闭的，因为 $\\mathbf { d } ^ { 2 } { \\boldsymbol { \\beta } } = 0$。用上链的语言，这些定义可表述如下：一个 $r$-上链 $\\alpha$ 若是一个闭微分形式，则称为 $r$-<u class=\"concept-term\" data-concept-identity=\"urn:uuid:c26a11a5-b8bb-4cd7-8920-cd092b71eb06\" data-concept-route=\"/concept-identities#concept-c26a11a5-b8bb-4cd7-8920-cd092b71eb06\" id=\"first-6a9d37016a96e22681a4-zh\">上闭链(cocycle)</u>；而若它是恰当的，则称为 $r$-<u class=\"concept-term\" data-concept-identity=\"urn:uuid:91f394ee-b446-4502-be7d-9d5169bdd21e\" data-concept-route=\"/concept-identities#concept-91f394ee-b446-4502-be7d-9d5169bdd21e\" id=\"first-0b1865b872f69033467f-zh\">上边界链(coboundary)</u>。我们将 $r$-上闭链的向量子空间记为 $Z ^ { r } ( M )$，将 $r$-上边界链的子空间记为 $B ^ { r } ( M )$",
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