Nrn1 Expression In Brain: Analysis In Individuals Diagnosed With Schizophrenia Patients And Healthy Subjects

The notion of D-sublocale is explored. This is the notion analogue to that of sublocale in the duality of TD-spaces. A sublocale S of a frame L is a D-sublocale if and only if the corresponding localic map preserves the property of being a covered prime. It is shown that for a frame L the system of those sublocales which are also D-sublocales form a dense sublocale SD(L) of the coframe S(L) of all its sublocales. It is also shown that the spatialization spD[SD(L)] of SD(L) consists precisely of those D-sublocales of L which are TD-spatial. Additionally, frames such that we have SD(L)≅P(ptD(L)) — that is, those such that D-sublocales perfectly represent subspaces — are characterized as those TD-spatial frames such that SD(L) is the Booleanization of S(L).