A Method for Constructing Coreflections for Nearness Frames

We provide a fairly general method, which is straightforward and widely applicable, for constructing some coreflections in the category of nearness frames. The method captures all coreflective subcategories with 1 1 coreflection maps; this includes the well-known uniform, totally bounded and separable coreflections. The primary application of this method answers in the affirmative the question of Dube and Mugochi ([15]) as to whether strong nearness frames are coreflective in nearness frames. We show that the strong coreflection can change the underlying frame, in contrast to Dube and Mugochi’s almost uniform coreflection in the category of interpolating nearness frames. The method also finds application in categories other than nearness frames, for instance, prenearness frames and nearness σ-frames. We conclude with an application to the unstructured setting where we recover the regular and completely regular coreflections in frames. Mathematics Subject Classification (2010) 06D22 18A40 54B30 54E15 54E17