Functor of extension in Hilbert cube and Hilbert space

• Autorzy: Piotr Niemiec
• Języki publikacji: EN

Abstrakty

EN

It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity, Lipschitz property, nonexpansiveness of maps in appropriate metrics.

Słowa kluczowe

EN

Z-set; Functor of extension; Hilbert cube; Fréchet space

Kategorie tematyczne

• 57N20: Topology of infinite-dimensional manifolds
• 54C20: Extension of maps
• 18B30: Categories of topological spaces and continuous mappings

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 6
• Strony: 887-895

Daty

wydano

2014-06-01

online

2014-03-19

Twórcy

autor

Piotr Niemiec

• Jagiellonian University

Bibliografia

• [1] Anderson R.D., Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc., 1966, 72(3), 515–519 http://dx.doi.org/10.1090/S0002-9904-1966-11524-0
• [2] Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383 http://dx.doi.org/10.1307/mmj/1028999787
• [3] Anderson R.D., McCharen J.D., On extending homeomorphisms to Fréchet manifolds, Proc. Amer. Math. Soc., 1970, 25(2), 283–289
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• [6] Banakh T.O., Topology of spaces of probability measures II. Barycenters of Radon probability measures and the metrization of the functors τ τ and \(\hat P\) , Mat. Stud., 1995, 5, 88–106 (in Russian)
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• [14] Niemiec P., Spaces of measurable functions, Cent. Eur. J. Math., 2013, 11(7), 1304–1316 http://dx.doi.org/10.2478/s11533-013-0236-6
• [15] Takesaki M., Theory of Operator Algebras. I, Encyclopaedia Math. Sci., 124, Springer, Berlin, 2002
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Identyfikatory

DOI

10.2478/s11533-013-0386-6