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Borel isomorphisms at the first level: Corrigenda et addenda

Published online by Cambridge University Press:  26 February 2010

J. E. Jayne  and
C. A. Rogers
J. E. Jayne
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT.
C. A. Rogers
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT.
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In recent work [2] we have investigated Borel isomorphisms at the first level, i.e. mappings that together with their inverses map Fσ-sets to Fσ-sets. We are grateful to Dr. F. Topsøe for writing to point out errors in the proofs of our Theorems 2.1, 2.2 and 2.3. The errors escaped our attention because we only wrote out the first step of a complicated inductive argument and carelessly and falsely claimed that the general step of the induction was similar to the first. To be more specific, in the proof of Theorem 2.1, although we do have

we do not, in general, have

Fortunately the proofs can be corrected.

Type
Research Article
Information
Mathematika , Volume 27 , Issue 2 , December 1980 , pp. 236 - 260
Copyright
Copyright © University College London 1980

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References

1.Engelking, R.. General topology (Warsaw, 1977).Google Scholar
2.Jayne, J. E. and Rogers, C. A.. “Borel isomorphisms at the first level I and II”, Mathematika, 26 (1979), 125–156 and 157–179.Google Scholar
3.Hurewicz, W.. “Relativ Perfekte Teile von Punktmengen und Mengen (A)”, Fund. Math., 12 (1928), 78–109.CrossRefGoogle Scholar
4.Ostrovskii, A. V.. “On nonseparable τ-A-sets and their mappings”, Soviet Math. Dokl., 17 (1976), 99–103.Google Scholar
5.Rogers, C. A., Jayne, J. E.Dellacherie, C.Topsøe, F.Hoffmann-Jorgensen, J.Martin, D. A.Kechris, A. S. and Stone, A. H.. Analytic Sets (Academic Press, London, 1980).Google Scholar
6.Saint-Raymond, J.. “Approximation des sous-ensembles analytiques par l'interieur”, C. R. Acad. Sc. Paris, Sér. A, 281 (1975), 85–87.Google Scholar
7.Talagrand, M.. “Sur les convexes compacts dont l'ensembles des points extrémaux est K-analytique”, Bull. Soc. Math. France, 107 (1979), 49–53.CrossRefGoogle Scholar
8.Telgársky, R.. “Spaces defined by topological games”, Fund. Math., 88 (1975), 195–223.CrossRefGoogle Scholar