TY - JOUR
ID - 15806
TI - Localic maps constructed from open and closed parts
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Pultr, Ales
AU - Picado, Jorge
AD - Department of Applied Mathematics and ITI, MFF, Charles University, Malostransk'e n'am. 24, 11800 Praha 1, Czech Republic.
AD - CMUC, Department of Mathematics, University of Coimbra, Apar\-ta\-do 3008, 3001-501 Coimbra, Portugal.
Y1 - 2017
PY - 2017
VL - 6
IS - Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)
SP - 21
EP - 35
KW - frame
KW - locale
KW - sublocale
KW - sublocale lattice
KW - open sublocale
KW - closed sublocale
KW - localic map
KW - preimage
KW - Boolean frame
KW - linear frame
DO -
N2 - Assembling a localic map $f\colon L\to M$ from localic maps $f_i\colon S_i\to M$, $i\in J$, defined on closed resp. open sublocales $(J$ finite in the closed case$)$ follows the same rules as in the classical case. The corresponding classical facts immediately follow from the behavior of preimages but for obvious reasons such a proof cannot be imitated in the point-free context. Instead, we present simple proofs based on categorical reasoning. There are some related aspects of localic preimages that are of interest, though. They are investigated in the second half of the paper.
UR - https://cgasa.sbu.ac.ir/article_15806.html
L1 - https://cgasa.sbu.ac.ir/article_15806_f90dc6ec251a402f3ff01305864296bd.pdf
ER -