Topologies on function spaces and hyperspaces


  • D. N. Georgiou University of Patras



Space, Hyperspace, Splitting topology, Admissible topology


Let Y and Z be two fixed topological spaces, O(Z) the family of all open subsets of Z, C(Y,Z) the set of all continuous maps from Y to Z, and OZ(Y ) the set {f−1(U) : f ϵ C(Y,Z) and U ϵ O(Z)}. In this paper, we give and study new topologies on the sets C(Y,Z) and OZ(Y ) calling (A,A0)-splitting and (A,A0)-admissible, where A and A0 families of spaces.


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Author Biography

D. N. Georgiou, University of Patras

Department of Mathematics


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How to Cite

D. N. Georgiou, “Topologies on function spaces and hyperspaces”, Appl. Gen. Topol., vol. 10, no. 1, pp. 159–171, Apr. 2009.