Topologies on the set of Borel maps of class α | Zendy

D.N. Georgiou | Zendy; A.C. Megaritis | Zendy; V.I. Petropoulos | Zendy

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Topologies on the set of Borel maps of class α

Author(s) -

D.N. Georgiou,

A.C. Megaritis,

V.I. Petropoulos

Publication year - 2015

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1501143g

Subject(s) - mathematics , uncountable set , borel set , class (philosophy) , polish space , borel equivalence relation , combinatorics , open set , discrete mathematics , borel measure , probability measure , artificial intelligence , mathematical analysis , countable set , computer science , separable space

Let ω1 be the first uncountable ordinal, α < ω1 an ordinal, and Y, Z two topological spaces. By Bα(Y,Z) we denote the set of all Borel maps of class α from Y into Z and by GZα(Y) the set consisting of all subsets f -1(U), where f Bα(Y,Z) and U is an open subset of Z. In this paper we introduce and investigate topologies on the sets Bα(Y,Z) and GZα(Y). More precisely, we generalize the results presented by Arens, Dugundji, Aumann, and Rao (see [1], [2], [3], and [10]) for Borel maps of class α.

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