Topologies on the set of Borel maps of class α

D.N. Georgiou, A.C. Megaritis, V.I. Petropoulos
2015 Filomat  
Let ω 1 be the first uncountable ordinal, α < ω 1 an ordinal, and Y, Z two topological spaces. By B α (Y, Z) we denote the set of all Borel maps of class α from Y into Z and by G Z α (Y) the set consisting of all subsets f −1 (U), where f ∈ B α (Y, Z) and U is an open subset of Z. In this paper we introduce and investigate topologies on the sets B α (Y, Z) and G Z α (Y). More precisely, we generalize the results presented by Arens, Dugundji, Aumann, and Rao (see [1], [2], [3], and [10]) for
more » ... , and [10]) for Borel maps of class α.
doi:10.2298/fil1501143g fatcat:tdkumdrw4belhmn2bpwgqk7uua