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Topologies on function spaces and hyperspaces
"... Abstract. 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, andOZ(Y) the set {f −1(U) : f ∈ C(Y, Z) and U ∈ O(Z)}. In this paper, we give and study new topologies on the sets C(Y, Z) and OZ(Y) calling (A,A0)spl ..."
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Abstract. 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, andOZ(Y) the set {f −1(U) : f ∈ C(Y, Z) and U ∈ 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. 2000 AMS Classification: 54C35