  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.
