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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Strongly rigid metrics and zero dimensionality

Author: Harold W. Martin
Journal: Proc. Amer. Math. Soc. 67 (1977), 157-161
MSC: Primary 54F50
MathSciNet review: 0454938
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Abstract: A metric d is strongly rigid if and only if $ d(x,y) \ne d(w,z)$ whenever the doubleton {x, y} is not equal to the doubleton {w, z}. It is shown that a nonempty metrizable space X admits a compatible strongly rigid metric if X has covering dimension zero and has cardinality equal to or less than that of the real line.

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

  • [1] B. Fitzpatrick and R. Ford, On the equivalence of small and large inductive dimension in certain metric spaces, Duke Math. J. 34 (1967), 33-39. MR 0205226 (34:5059)
  • [2] L. Janos, A metric characterization of zero-dimensional spaces, Proc. Amer. Math. Soc. 31 (1972), 268-270. MR 0288739 (44:5935)
  • [3] J. Nagata, Modern dimension theory, Wiley, New York, 1965. MR 0208571 (34:8380)

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Keywords: Strongly rigid metric, zero dimensional space
Article copyright: © Copyright 1977 American Mathematical Society

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