关于子空间的超空间拓扑

For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X : (CL(A), T(A))→(CL(X),T(X)) defined by iA,x(F) = ^-F whenever F ∈ CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.

On the Behaviors of Hyperspace Topologies for Subspaces