In this paper, we introduce two new notions of S-continuous information systems and S-abstract bases which provide concrete representations of stably continuous semi-lattices. We shed light on how the states of an S-continuous information system and the round ideal completion of an S-abstract basis form a stably continuous semi-lattice, respectively. Then we obtain two representation theorems for stably continuous semi-lattices. What is more, we show the equivalence of the categories corresponding to these three structures.

中文翻译：

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信息系统和抽象库表示稳定连续的半格

在本文中，我们介绍了S-连续信息系统和S-抽象基的两个新概念，它们提供了稳定连续半格的具体表示。我们阐明了S连续信息系统的状态和S抽象基础的圆形理想完成如何分别形成稳定连续的半格。然后我们获得了两个关于连续连续半格的表示定理。此外，我们显示了与这三个结构相对应的类别的等效性。