Web空间与全球Web空间：域论的拓扑方面
Web spaces and worldwide web spaces: topological aspects of domain theory
AI总结：
本文通过补片空间和扇形空间刻画Web空间及C-空间，推广连续格定理至非完全偏序集，并研究其基数不变量。
摘要：
Web空间、宽Web空间和全球Web空间（别名C-空间）提供了连续域的有用推广。我们给出了这些空间及其补片空间的新刻画，这些补片空间是通过将原始拓扑与具有对偶特化序的第二拓扑合并而得到的；这些补片空间具有良好的凸性和分离性质，并决定了原始Web空间。C-空间范畴与扇形空间范畴具体同构；扇形空间是某些具有扇形邻域基的拟序空间，这些扇形是通过从主对偶理想中删除有限个主对偶理想而得到的。我们的方法对域论有有用的推论，因为T$_0$ Web空间恰好是局部逼近理想扩张的广义Scott空间，而T$_0$ C-空间恰好是全局逼近且插值的理想扩张的广义Scott空间。我们将连续格作为具有T$_2$ Lawson拓扑的meet-连续格的刻画以及紧半格基本定理推广到非完全偏序集。最后，研究了所涉及对象的密度和权重等基数不变量。
英文摘要：
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.
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