集值映射空间各种收敛拓扑的统一描述

ON AN UNIFIED DESCRIPTION FOR TOPOLOGIES OF CONVERGENCES FOR MULTIFUNCTION SPACES

文献[1]首次刻画了集值映射空间中关于各种收敛性的网的极限类及与之对应的各种邻近结构,本文则进一步探计这些收敛性能否确定与之相伴的拓扑。首先,我们借助一致空间的一致覆盖族定义了一致空间中的(*)包含动算并应用它给出了建立集值映射空间中各种收敛概念及其相伴拓扑的一种统一的框架。其次,我们具体论述了集值映射空间中十二种收敛性的相伴拓扑。最后,我们指出上述拓扑中的四种相伴拓扑均可分别重合于集值映射空间的某个一致拓扑。

In this paper we make use of a uniform covering system of a uniform spac to define the (*) containing operations and apply it to constitute topologies of various kinds of convergences for multifunction mapping spaces by an unified frame Besides, we point out that the topology of convergence at a point, point convergence, uniform convergence or uniform convergence on every membter of a family coincides with a certain uniform topology for multifunction spaces.