2024/07/18 by Mbekezeli Nxumalo, Nxumalo, Mbekezeli
Arts and Humanities · #06D22 #FOS: Mathematics #General Topology (math.GN) #Linguistics and Cultural Studies
paper · pdf · doi:10.48550/arxiv.2407.13400
openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study some variants of remote sublocales, namely sublocales that are remote from dense sublocales and those that are *remote from dense sublocales. We show that the coframe of sublocales coincides with the collection of all sublocales remote from the Booleanization. Furthermore, the supplement of the Booleanization of any locale is the largest sublocale *remote from the Booleanization. We give conditions on localic maps such that their induced localic image and pre-image functions preserve sublocales that are remote (resp. *remote) from dense sublocales. We introduce new types of localic maps called f-remote preserving maps.