Abstrakt
Sublocales that are joins of closed ones constitute a frame S-Vc(L) embedded as a sup-sublattice into the coframe S(L) of sublocales of L. We prove that in the case of subfit L it is a subcolocale of S(L), that it is then a Boolean algebra and in fact precisely the Booleanization of S(L).
In case of a T-1-space X, S-Vc(Q(X)) picks precisely the sublocales corresponding to induced subspaces. In linear L and more generally if L is also a coframe, S-Vc(L) is both a frame and a coframe, but with trivial exceptions not Boolean and not a subcolocale of S(L).