Strongly rigid metrics and zero dimensionality
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- by Harold W. Martin PDF
- Proc. Amer. Math. Soc. 67 (1977), 157-161 Request permission
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
- Ben Fitzpatrick Jr. and Ralph M. Ford, On the equivalence of small and large inductive dimension in certain metric spaces, Duke Math. J. 34 (1967), 33–37. MR 205226
- Ludvík Janoš, A metric characterization of zero-dimensional spaces, Proc. Amer. Math. Soc. 31 (1972), 268–270. MR 288739, DOI 10.1090/S0002-9939-1972-0288739-5
- Jun-iti Nagata, Modern dimension theory, Bibliotheca Mathematica, Vol. VI, Interscience Publishers John Wiley & Sons, Inc., New York, 1965. Edited with the cooperation of the “Mathematisch Centrum” and the “Wiskundig Genootschap” at Amsterdam. MR 0208571
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 67 (1977), 157-161
- MSC: Primary 54F50
- DOI: https://doi.org/10.1090/S0002-9939-1977-0454938-7
- MathSciNet review: 0454938