Representations of stably continuous semi-lattices by information systems and abstract bases

Abstract

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.