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The notion of \emph{D-sublocale} is explored. This is the notion analogue tothat of sublocale in the duality of $T_D$spaces. A sublocale $S$ of a frame $L$is a D-sublocale if and only if the corresponding localic map preserves theproperty of being a covered prime. It is shown that for a frame $L$ the systemof those sublocales which are also D-sublocales form a dense sublocale$\mathsf{S}_D(L)$ of the coframe $\mathsf{S}(L)$ of all its sublocales. It isalso shown that the spatialization $\mathsf{sp}_D[\mathsf{S}_D(L)]$ of$\mathsf{S}_D(L)$ consists precisely of those D-sublocales of $L$ which are$T_D$-spatial. Additionally, frames such that we have $\mathsf{S}_D(L)\cong\mathcal{P}(\mathsf{pt}_D(L))$ -- that is, those such that D-sublocalesperfectly represent subspaces -- are characterized as those $T_D$-spatialframes such that $\mathsf{S}_D(L)$ is the Booleanization of \mathsf{S}(L).

The coframe of D-sublocales of a locale and the $T_D$ duality