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ON A THEOREM OF ARVANITAKIS

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

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)
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Abstract

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 maps 46E40: Spaces of vector- and operator-valued functions
Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013 , pp. 250 - 256
Copyright
Copyright © University College London 2012

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References

[1]Arvanitakis, A., A simultaneous selection theorem. Preprint.Google Scholar
[2]Banakh, T., Topology of spaces of probability measures I: The functors P τ and . Mat. Stud. 5 (1995), 65–87 (in Russian).Google Scholar
[3]Banakh, T., Topology of spaces of probability measures II: Barycenters of probability radon measures and metrization of the functors P τ and . Mat. Stud. 5 (1995), 88–106 (in Russian).Google Scholar
[4]Chigogidze, A., Extension of normal functors. Vestnik Moskov. Univ. Ser. I Mat. Mekh. 6 (1984), 23–26 (in Russian).Google Scholar
[5]Choban, M., Topological structures of subsets of topological groups and their quotient spaces. Mat. Issl. 44 (1977), 117–163 (in Russian).Google Scholar
[6]Dugundji, J., An extension of Tietze’s theorem. Pacific J. Math. 1 (1951), 353–367.CrossRefGoogle Scholar
[7]Engelking, R., General Topology, Polish Scientific Publishers (Warsaw, 1977).Google Scholar
[8]Engelking, R., Theory of Dimensions: Finite and Infinitite, Heldermann (Lemgo, 1995).Google Scholar
[9]Heath, R. and Lutzer, D., Dugundji extension theorems for linearly ordered spaces. Pacific J. Math. 55(2) (1974), 419–425.CrossRefGoogle Scholar
[10]Michael, E., Continuous selections I. Ann. of Math. (2) 63 (1956), 361–382.CrossRefGoogle Scholar
[11]Michael, E., Continuous selections II. Ann. of Math. (2) 64 (1956), 362–380.CrossRefGoogle Scholar
[12]Pelczyński, A., Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions. Dissertationes Math. 58 (1968), 1–89.Google Scholar
[13]Repovš, D. and Semenov, P., Continuous Selections of Multivalued Mappings (Mathematics and its Applications 455), Kluwer Academic Publishers (Dordrecht, 1998).CrossRefGoogle Scholar
[14]Repovš, D., Semenov, P. and Shchepin, E., On zero-dimensional Millutin maps and Michael selection theorems. Topology Appl. 54 (1993), 77–83.CrossRefGoogle Scholar
[15]Schaefer, H., Topological Vector Spaces (Graduate Texts in Mathematics 3), Springer (New York, 1971).CrossRefGoogle Scholar
[16]Valov, V., Linear operators with compact supports, probability measures and Milyutin maps. J. Math. Anal. Appl. 370 (2010), 132–145.CrossRefGoogle Scholar