标题： 纤维紧化和交换与非交换拓扑中的广义极限 显示英文标题

标题： Fibrewise compactifications and generalised limits in commutative and noncommutative topology

摘要： 我们分别在局部紧Hausdorff空间及其连续映射的框架下，以及在$C^*$-代数和非退化多重乘子值$*$-同态的平行框架下引入纤维紧化。在这两种情况下，我们都利用纤维紧化来定义受控极限。在拓扑学设定中，受控极限推广了经典的逆向极限，使得所得的极限空间仍然保持局部紧性；例子包括有向图的路径空间。在算子代数设定中，受控极限实现了多重乘子值$*$-同态的直接极限构造；例子包括相对Cuntz-Pimsner代数的核心。 显示英文摘要

摘要： We introduce fibrewise compactifications in both the setting of locally compact Hausdorff spaces and continuous maps, and the parallel setting of $C^*$-algebras and nondegenerate multiplier-valued $*$-homomorphisms. In both situations, we use fibrewise compactifications to define regulated limits. In the topological setting, regulated limits extend classical inverse limits so that the resulting limit space remains locally compact; examples include the path spaces of directed graphs. In the operator-algebraic setting, regulated limits realise a direct-limit construction for multiplier-valued $*$-homomorphisms; examples include the cores of relative Cuntz-Pimsner algebras.