A note on information systems for continuous semi-lattices

Abstract

Wang et al. recently provided a representation for continuous semi-lattices by SL-information systems and raised a question in the conclusion section of [15]. That is, whether a modification of the notion of an approximable mapping can be made so that an equivalence to the category of continuous semi-lattices is obtained. This category has Scott-continuous functions that respect non-empty finite meets as morphisms. In this note, we solve this problem by introducing the concept of SL-approximable mappings between SL-information systems. As an application, we propose the BC-approximable mappings between BC-information systems and establish a categorical equivalence between BC-information systems with BC-approximable mappings and bounded-complete domains with Scott-continuous functions that preserve non-empty infima.