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2014 | 12 | 6 | 887-895
Tytuł artykułu

Functor of extension in Hilbert cube and Hilbert space

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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
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
6
Strony
887-895
Opis fizyczny
Daty
wydano
2014-06-01
online
2014-03-19
Twórcy
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
  • [4] Aronszajn N., Panitchpakdi P., Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math., 1956, 6(3), 405–439 http://dx.doi.org/10.2140/pjm.1956.6.405
  • [5] Banakh T.O., Topology of spaces of probability measures I. The functors τ τ and \(\hat P\) , Mat. Stud., 1995, 5, 65–87 (in Russian)
  • [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)
  • [7] Bessaga Cz., Pełczyński A., On spaces of measurable functions, Studia Math., 1972, 44, 597–615
  • [8] Bessaga Cz., Pełczyński A., Selected Topics in Infinite-Dimensional Topology, IMPAN Monogr. Mat., 58, PWN, Warsaw, 1975
  • [9] Chapman T.A., Deficiency in infinite-dimensional manifolds, General Topology Appl., 1971, 1, 263–272 http://dx.doi.org/10.1016/0016-660X(71)90097-3
  • [10] Halmos P.R., Measure Theory, Van Nostrand, New York, 1950 http://dx.doi.org/10.1007/978-1-4684-9440-2
  • [11] Keller O.-H., Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann., 1931, 105, 748–758 http://dx.doi.org/10.1007/BF01455844
  • [12] Klee V.L. Jr., Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc., 1952, 3(3), 484–487 http://dx.doi.org/10.1090/S0002-9939-1952-0047250-4
  • [13] Kuratowski K., Mostowski A., Set Theory, 2nd ed., PWN, Warsaw, 1976
  • [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
  • [16] Toruńczyk H., Characterizing Hilbert space topology, Fund. Math., 1981, 111(3), 247–262
  • [17] Toruńczyk H., A correction of two papers concerning Hilbert manifolds: “Concerning locally homotopy negligible sets and characterization of l 2-manifolds” and “Characterizing Hilbert space topology”, Fund. Math., 1985, 125, 89–93
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0386-6
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