无点滤子收敛

Convergence of Filters without Points

我们在ｌｏｃａｌｅ上定义了一种新的滤子收敛概念．对空间式ｌｏｃａｌｅ，这种收敛与拓扑收敛等价，并且适应于任意ｌｏｃａｌｅ．作为应用，我们给出了ｌｏｃａｌｅ紧的程度的刻划和 Ｃａｕｃｈｙ完备性的描述．

We introduce a new definition of convergence of filters on a locale, which is equivalent to topological convergence on spatial lovales and can be applied to any locale. As applications, some characteriztions of compactness and description of Cauchy completeness are obtained.