论文标题
越野散落的普里斯特利空间超级空间
Vietoris hyperspaces of scattered Priestley spaces
论文作者
论文摘要
我们研究了Priestley空间的封闭式和封闭式最终组的越野越高。我们对Skula拓扑特别感兴趣。如果拓扑空间是\ emph {skula}，如果其拓扑是通过另一个拓扑的开放集的差异而产生的。紧凑型Skula空间被散布，此外，具有与拓扑结构兼容的天然有充分的订单，即，它是Priestley空间。我们的主要目标之一是调查普里斯特利一般空间的越野范围，何时它们的拓扑为skula并计算相关的序数等级。我们将结果应用于基于某些几乎不相交的家族，尤其是Lusin家族和梯子系统的散落的紧凑空间。
We study Vietoris hyperspaces of closed and closed final sets of Priestley spaces. We are particularly interested in Skula topologies. A topological space is \emph{Skula} if its topology is generated by differences of open sets of another topology. A compact Skula space is scattered and moreover has a natural well-founded ordering compatible with the topology, namely, it is a Priestley space. One of our main objectives is investigating Vietoris hyperspaces of general Priestley spaces, addressing the question when their topologies are Skula and computing the associated ordinal ranks. We apply our results to scattered compact spaces based on certain almost disjoint families, in particular, Lusin families and ladder systems.
