# OnHyperspaces of Subspaces

Cheng Hou, Ji (1998) OnHyperspaces of Subspaces. Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., 76-77. pp. 139-153.

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atti_3_1998-1999_139.pdf - Submitted Version

For a topological space $X$ we denote by $CL(X)$ the collection of all non-empty closed subsets of $X$. Suppose we have a map $J$ which assigns in some coherent way to every topological space $X$ some topology $J \ (X)$ on $CL(X)$. In this paper we study continuity and inverse continuity of the map $i_{A,X}:(CL(A),J(A))\rightarrow \(CL(X),J(X))$ defined by $i_{A,X}(F)=\bar F\$ whenever $F \in \ CL(A)$ for various assignment $J$; in particular, for locally finite topology, upper Kuratowski topology, or Attouch-Wets topology, etc.