论文标题
关于Kakutani $ C（x）$的封闭线性议法的特征 - 重新审视
On Kakutani's characterization of the closed linear sublattices of $C(X)$ -- Revisited
论文作者
论文摘要
在他的论文中[抽象$（m）$ - 空间的具体表示。 （连续函数空间的表征。），Ann。数学，$ 42（2）$（$ 1941 $），$ 994 $ - $ 1024 $。]，S。Kakutani对封闭的线性议法的封闭式sublattices进行了有趣的代表，该空间是紧凑型Hausdorff空间的实用值连续功能的空间，这是由一组Algebraic关系确定的。在此简短说明中，我们提供了一个简单的证明，而无需使用任何深刻的晶格理论或功能分析结果，从而使该证明甚至可以访问本科生。
In his paper [Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math., $42 (2)$ ($1941$), $994$--$1024$.], S. Kakutani gave an interesting representation of the closed linear sublattices of the space of real-valued continuous functions on a compact Hausdorff space, which is determined by a set of algebraic relations. In this short note, we present a simple proof of this representation without using any profound lattice theory or functional analysis results, making this proof accessible even to undergraduate students.
