一句话：在 T0 空间框架下研究 Scott 收敛的拓扑化，并给出 I-收敛结构成为拓扑收敛的必要与充分条件。
本文回应 Lawson 关于在更一般的 T0 空间而非仅偏序集背景下发展 domain theory 的倡议，尝试建立 Scott 收敛定理的拓扑版本。作者关注 Scott 收敛 S 何时是拓扑收敛这一经典问题。为此，他们利用 ID replacement principle 构造 domain theory 概念的拓扑类比：以 I-连续空间对应连续偏序集，以 I-收敛对应 S-收敛。在此基础上，论文引入两个新的拓扑概念，即 I-稳定空间与 DI 空间，并由此给出收敛结构 I 为拓扑收敛的一些必要条件和充分条件。
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the Scott Convergence Theorem, i.e., an order-theoretic characterisation of those posets for which the Scott-convergence $\mathcal{S}$ is topological. To do this, we make use of the $\mathcal{ID}$ replacement principle to create topological analogues of well-known domain-theoretic concepts, e.g., $\mathcal{I}$-continuous spaces correspond to continuous posets, as $\mathcal{I}$-convergence corresponds to $\mathcal{S}$-convergence. In this paper, we consider two novel topological concepts, namely, the $\mathcal{I}$-stable spaces and the $\mathcal{DI}$ spaces, and as a result we obtain some necessary (respectively, sufficient) conditions under which the convergence structure $\mathcal{I}$ is topological.