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


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.