一句话：给出 web、wide web 与 worldwide web 空间及 patch 空间的新刻画，并联系连续域、Scott 空间与 fan 空间。
本文研究 web 空间、wide web 空间与 worldwide web 空间（又称 C-空间）及其 patch 空间，它们是连续 domain 的有用推广。作者把原拓扑与具有对偶特殊化序的第二拓扑结合，构造 patch 空间，证明其具有良好凸性与分离性质，并能决定原空间。方法上，文章给出 web/C-空间的新刻画，并证明 C-空间范畴具体同构于 fan 空间范畴，后者以主对偶理想删去有限个主对偶理想所得邻域基为特征。该视角直接联系 domain theory：T0 web 空间恰为局部逼近理想扩张的广义 Scott 空间，T0 C-空间恰为全局逼近且插值理想扩张的广义 Scott 空间。文章还将连续格的 Lawson 拓扑刻画与紧半格基本定理推广到非完备偏序集，并研究密度、权等基数不变量。
Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology with a second topology having the dual specialization order; these patch spaces possess good convexity and separation properties and determine the original web spaces. The category of C-spaces is concretely isomorphic to the category of fan spaces; these are certain quasi-ordered spaces having neighborhood bases of fans, obtained by deleting a finite number of principal dual ideals from a principal dual ideal. Our approach has useful consequences for domain theory, because the T$_0$ web spaces are exactly the generalized Scott spaces of locally approximating ideal extensions, and the T$_0$ C-spaces are exactly the generalized Scott spaces of globally approximating and interpolating ideal extensions. We extend the characterization of continuous lattices as meet-continuous lattices with T$_2$ Lawson topology and the Fundamental Theorem of Compact Semilattices to non-complete posets. Finally, cardinal invariants like density and weight of the involved objects are investigated.Comment: 36 pages, 1 figure, 8 diagrams. arXiv admin note: text overlap with arXiv:1607.04721