Topologies on function spaces and hyperspaces

D.N. Georgiou


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.


Space; Hyperspace; Splitting topology; Admissible topology

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