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Proceedings of the American Mathematical Society

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$ s$ admits an injective metric


Author: John R. Isbell
Journal: Proc. Amer. Math. Soc. 28 (1971), 259-261
MSC: Primary 54.35; Secondary 46.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0282333-7
MathSciNet review: 0282333
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Abstract: There is an injective metric space homeomorphic with a countably infinite product of lines.


References [Enhancements On Off] (What's this?)

  • [1] R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515-519. MR 32 #8298. MR 0190888 (32:8298)
  • [2] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439; correction, ibid. 7 (1957), 1729. MR 18, 917; MR 19, 1069. MR 0084762 (18:917c)
  • [3] J. R. Isbell, Six theorems about injective metric spaces, Comment. Math. Helv. 39 (1964), 65-76. MR 32 #431. MR 0182949 (32:431)
  • [4] M. I. Kadec, Topological equivalence of all separable Banach spaces, Dokl. Akad. Nauk SSSR 167 (1966), 23-25=Soviet Math. Dokl. 7 (1966), 319-322. MR 34 #1828. MR 0201951 (34:1828)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0282333-7
Keywords: Metric space, injective, contraction
Article copyright: © Copyright 1971 American Mathematical Society

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