范畴测度、$C(K)^δ$与超Stonean空间的对偶
Category measures, the dual of $C(K)^δ$ and hyper-Stonean spaces
摘要：
对于紧致T2空间$K$，我们给出了$C(K)^δ$的对偶，即$K$上连续实值函数的巴拿赫格$C(K)$的Dedekind完备化.利用Oxtoby范畴测度刻画了$σ$ -序连续和序连续的泛函.这导致了超斯通空间的一个纯粹的拓扑特征。
英文摘要：
For a compact Hausdorff space $K$, we give descriptions of the dual of $C(K)^δ$, the Dedekind completion of the Banach lattice $C(K)$ of continuous, real-valued functions on $K$. We characterize those functionals which are $σ$-order continuous and order continuous, respectively, in terms of Oxtoby's category measures. This leads to a purely topological characterization of hyper-Stonean spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
