Abstract
The concepts of Booleanization and of smallest dense quotient are explored in the context of d-frames. These two notions coincide for frames, but bitopologically they turn out to be different. The approach followed here is different from that in (Moshier in On Isbell’s density theorem for bitopological pointfree spaces I 273:106962, 2020), in which the smallest dense extremal epimorphism of a d-frame is described. Here, we consider the lattice of all quotients of a d-frame, extremal and nonextremal. Here, it is shown that for corrigible d-frames there is a smallest dense quotient, and it is shown that this coincides with the Booleanization of a d-frame: this is a construction which, as in the frame theoretical case, gives us the Boolean reflection of a d-frame in a suitable subcategory of the category of d-frames.
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Communicated by: Maria Manuel Clementino.
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Suarez, A.L. The Booleanization of a d-frame. Appl Categor Struct 30, 485–497 (2022). https://doi.org/10.1007/s10485-021-09663-9
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DOI: https://doi.org/10.1007/s10485-021-09663-9