On the Behaviors of Hyperspace Topologies for Subspaces  

作　　者：侯吉成 高智民 

机构地区：[1]Department of Mathematics, Shantou University, Shantou, Guangdong, 515063 Department of Mathematics and Information Science, Yantai University, Yantai, Shandong, 264005 [2]Department of Mathematics, Shenzhen University, Shenzhen, Guangdong, 518060or 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 [3]in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.

出　　处：《Northeastern Mathematical Journal》2003年第4期295-305,共11页东北数学（英文版）

基　　金：Foundation item: The NNSF (10171043) of China.

摘　　要：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.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.

关 键 词：hyperspace topology SUBSPACE inverse continuity 

分 类 号：O189[理学—数学]