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arXiv · 2209.04140

On Kakutani's characterization of the closed linear sublattices of $C(X)$ -- Revisited

Teena Thomas
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Abstract

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.

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Teena Thomas. 2022-09-09. On Kakutani's characterization of the closed linear sublattices of $C(X)$ -- Revisited. https://arxiv.org/abs/2209.04140

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