Remarks on general monotonic neighbourhood frames

Abstract

In this paper we shall discuss some classes of general monotonic neighbourhood frames, or general m-frames. We shall study the classes of point-compact, image compact and replete general m-frames, and the relationships between them. The variety of Boolean algebras with a monotonic modal operator is dually equivalent to two classes of descriptive general m-frames. In this paper we shall clarify this phenomenon showing that there exists a bijective correspondence between these two classes. We shall also prove that the notions of point-compact, and image-compact monotonic frames are preserved by strong bounded morphisms. Also, we will prove some preservation results on general subframes.