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        "quote": "现代数学的一条基本思想是：若把空间 $M$ 看作由若干点组成，那么理解 $M$ 的一种方式是研究<span id=\"concept-1-function-space\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-function-space\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:b2da5ce9-fdbc-4d32-9495-60eba58b0cab\" data-concept-route=\"/concept-identities#concept-b2da5ce9-fdbc-4d32-9495-60eba58b0cab\" id=\"first-467fca2b7844dc4bfc62-zh\">函数空间(function space)</u> $F(M)$，也就是定义在 $M$ 上的函数所构成的集合。这样便将问题“<span id=\"concept-1-linearize\" class=\"block-anchor\"></span><span id=\"concept-1-linearization\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-linearization\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:39c83087-8f6e-4028-bca4-e15886984c77\" data-concept-route=\"/concept-identities#concept-39c83087-8f6e-4028-bca4-e15886984c77\" id=\"first-add16b5bc60391c7391b-zh\">线性化(linearize)</u>”了，因为无论原点集具有怎样的几何结构，函数空间都是向量空间。若点集有限，函数空间就是有限维向量空间；一般而言，它是无限维的，还需要进一步说明所考虑的函数空间类型（例如连续函数、可微函数或范数有限的函数）。",
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