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ON A THEOREM OF ARVANITAKIS

Part of:Maps and general types of spaces defined by mapsLinear function spaces and their duals

Published online by Cambridge University Press:  02 August 2012

Vesko Valov
Vesko Valov*
Affiliation:
Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, PO Box 5002, North Bay, Ontario, Canada P1B 8L7 (email: veskov@nipissingu.ca)

Abstract

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Arvanitakis [A simultaneous selection theorem. Preprint] recently established a theorem which is a common generalization of Michael’s convex selection theorem [Continuous selections I. Ann. of Math. (2) 63 (1956), 361–382] and Dugundji’s extension theorem [An extension of Tietze’s theorem, Pacific J. Math.1 (1951), 353–367]. In this note we provide a short proof of a more general version of Arvanitakis’s result.

MSC classification

Secondary:54C60: Set-valued maps46E40: Spaces of vector- and operator-valued functions

Information

Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013, pp. 250 - 256
Copyright
Copyright © University College London 2012

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