Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 6 Speical Issue on the Occasion of Banaschewski's 90th Birthday (I) 2017 01 01 Localic maps constructed from open and closed parts 21 35 15806 EN Ales Pultr Department of Applied Mathematics and ITI, MFF, Charles University, Malostransk'e n'am. 24, 11800 Praha 1, Czech Republic. Jorge Picado CMUC, Department of Mathematics, University of Coimbra, Apar\-ta\-do 3008, 3001-501 Coimbra, Portugal. 0000-0001-7837-1221 Journal Article 2016 05 02 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. https://cgasa.sbu.ac.ir/article_15806_520a4a78c0a273d6505cc3970f556450.pdf