Sublocale sets and sublocale lattices

J. Picado, A. Pultr

Address. Departamento de Matem\'{a}tica, Universidade de Coimbra, Apartado 3008, Coimbra, Portugal
Department of Applied Mathematics and ITI, MFF, Charles University, Praha, Czech Republic

E-mail: picado@mat.uc.pt, pultr@kam.ms.mff.cuni.cz

Abstract. We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell's Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.

AMSclassification. 34K15, 34K25; Secondary 39B99.

Keywords. Frames, sublocales, coframe of sublocales, fitness and subfitness.