The notion of D-sublocale is explored. This is the notion analogue to that 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 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 ${\mathsf{S}}_D(L)$ of the coframe $\mathsf{S}(L)$ of all its sublocales. It is also 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-sublocales perfectly represent subspaces — are characterized as those $T_D$-spatial frames such that ${\mathsf{S}}_D(L)$ is the Booleanization of $\mathsf{S}(L)$.

探索了D-sublocale的概念。这与子语言环境的二元性的概念类似${Ť}_d$-空间。甲sublocale小号的帧的大号是d -sublocale当且仅当相应的localic地图保留的是一个盖的灌注属性。结果表明，对于帧L，那些也是D-子区域的子区域的系统形成一个密集的子区域${\mathsf{小号}}_d（\mathrm{大号}）$ 共框架的 $\mathsf{小号}（\mathrm{大号}）$其所有子区域。还表明，空间化${\mathsf{SP}}_d[{\mathsf{小号}}_d（\mathrm{大号}）]$ 的 ${\mathsf{小号}}_d（\mathrm{大号}）$由精确的那些d的-sublocales大号其是${Ť}_d$-空间。此外，这样的框架${\mathsf{小号}}_d（\mathrm{大号}）\cong \mathcal{P}（{\mathsf{pt}}_d（\mathrm{大号}））$—即那些使D -sublocales完美表示子空间的特征—${Ť}_d$-空间框架 ${\mathsf{小号}}_d（\mathrm{大号}）$ 是的布尔化 $\mathsf{小号}（\mathrm{大号}）$。