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On extending mappings into nonlocally convex linear metric spaces

Author: T. Dobrowolski
Journal: Proc. Amer. Math. Soc. 93 (1985), 555-560
MSC: Primary 54C55; Secondary 46E30, 54D45, 57N17
MathSciNet review: 774022
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Abstract: It is proved that the following spaces are absolute retracts: every $ F$-space with a Schauder basis and certain function spaces along with their subgroups of integer-valued elements. It is also observed that for every $ \sigma $-compact convex set, the absolute extension property for compacta implies the AR-property.

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  • [1] C. Bessaga and T. Dobrowolski, Some problems in the border of functional analysis and topology, Proc. Internat. Conf. Geometric Topology (Warsaw, 1978), PWN, Warsaw, 1980, pp. 39-42.
  • [2] C. Bessaga and A. Pełczyński, Selected topics in infinite-dimensional topology, PWN, Warsaw, 1975.
  • [3] D. W. Curtis, T. Dobrowolski and J. Mogilski, Some applications of the topological characterizations of the sigma-compact spaces $ l_2^f$ and $ \Sigma $, Trans. Amer. Math. Soc. 284 (1984), 837-846. MR 743748 (86i:54035)
  • [4] T. Dorowolski and H. Toruńczyk, On metric linear spaces homeomorphic to $ {l_2}$ and convex sets homeomorphic to $ Q$, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 27 (1979), 883-887. MR 616181 (82j:57010)
  • [5] -, Separable complete ANR's admitting group structures are Hilbert manifolds, Topology Appl. 12 (1981), 229-235. MR 623731 (83a:58007)
  • [6] O. Hanner, Some theorems on absolute retracts, Ark. Mat. 1 (1951), 389-408. MR 0043459 (13:266d)
  • [7] W. E. Haver, A covering property for metric spaces, VPI Topology Conf. (R. F. Dickman and P. Fletcher, eds.), Lecture Notes in Math., vol. 375, Springer-Verlag, New York, 1974, pp. 108-113. MR 0365504 (51:1756)
  • [8] J. Ishii, On the admissibility of function spaces, J. Fac. Sci. Hokkaido Univ. 19 (1965), 49-55. MR 0188765 (32:6201)
  • [9] V. L. Klee, Shrinkable neighborhoods in Hausdorff linear spaces, Math. Ann. 141 (1960), 281-285. MR 0131149 (24:A1003)
  • [10] -, Leray-Schauder theory without local convexity, Math. Ann. 141 (1960), 286-296. MR 0131150 (24:A1004)
  • [11] K. Kuratowski, Sur quelques problèmes topologiques concernant le prolongement des fonctions continues, Colloq. Math. 2 (1951), 186-191. MR 0048791 (14:70d)
  • [12] W. A. J. Luxemburg and A. C. Zaanen, Notes on Banach function spaces, Indag. Math. 25 (1963), 135-147. MR 0149231 (26:6723a)

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Keywords: Convex sets, locally contractible groups, ANR spaces, ANE spaces
Article copyright: © Copyright 1985 American Mathematical Society

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