We introduce the notion of (maximal) multi-truncations on a vector lattice as a generalization of the notion of truncations, an object of recent origin. We obtain a Johnson–Kist type representation of vector lattices with maximal multi-truncations as vector lattices of almost-finite extended-real continuous functions. The spectrum that allows such a representation is a particular set of prime ideals equipped with the Hull–Kernel topology. Various representations from the existing literature will appear as special cases of our general result.

中文翻译：

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截断向量格的Johnson-Kist类型表示

我们引入矢量格上的（最大）多截断概念，作为对截断概念（最近起源的对象）的概括。我们获得具有最大多重截断的向量格的Johnson-Kist类型表示，作为几乎有限的扩展-实连续函数的向量格。允许这种表示的频谱是配备了赫尔-内核拓扑的一组特定的主要理想。现有文献中的各种表示形式将作为我们总体结果的特例出现。