论文标题
在两种类型的二进制关系的超滤波器扩展
On two types of ultrafilter extensions of binary relations
论文作者
论文摘要
存在两种不同类型的二进制关系的超滤波器扩展，一种是在通用代数和模态逻辑中发现的，另一种是在模型理论和Ultrafilters的代数中发现的。我们表明，后一种类型的扩展已正确包含在前者的扩展中，并描述了它们与关系代数操作的相互作用。然后，我们提供了两种扩展的拓扑特征，并表明较大的扩展将超滤器的空间连续映射到具有越野拓扑的过滤器的空间中。
There exist two distinct types of ultrafilter extensions of binary relations, one discovered in universal algebra and modal logic, and another, in model theory and algebra of ultrafilters. We show that the extension of the latter type is properly included in the extension of the former type, and describe their interaction with the relation algebra operations. Then we provide topological characterizations of both extensions and show that the larger extension continuously maps the space of ultrafilters into the space of filters endowed with the Vietoris topology.
