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Borel selectors for upper semi-continuous multi-valued functions

Part of: Normed linear spaces and Banach spaces; Banach lattices

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, London, WC1E 6BT
C. A. Rogers
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
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Extract

In our paper [12[ we made extensive use of the details of the proofs given in our earlier paper [11], and, in particular, we claimed that Lemma 3 of [11] holds, not just when Y is a metric space, but also when Y is a Hausdorff space, provided X × Y is a Fréchet space. In a corrigendum to [11], we give a corrected version of this Lemma 3, but it seems to depend, in an essential way, on the assumption that Y is a metric space, or at least a perfectly normal space. In this note we show that a modified version of this Lemma 3 enables us to justify all the theorems in [12] by use of a modified method of selection.

MSC classification

Secondary: 46B99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 32 , Issue 2 , December 1985 , pp. 324 - 337
Copyright
Copyright © University College London 1985

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