Metric transforms and the hyperbolic four-point property

Valentine, Joseph E.; Wayment, Stanley G.

doi:10.1090/S0002-9939-1972-0290254-X

Metric transforms and the hyperbolic four-point property
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by Joseph E. Valentine and Stanley G. Wayment

Proc. Amer. Math. Soc. 31 (1972), 232-234

DOI: https://doi.org/10.1090/S0002-9939-1972-0290254-X

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Abstract:

The purpose of this paper is to show that any metric space is homeomorphic to a metric space with each quadruple of its points congruently imbeddable in three-dimensional hyperbolic space.

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Bibliographic Information

Journal: Proc. Amer. Math. Soc. 31 (1972), 232-234
DOI: https://doi.org/10.1090/S0002-9939-1972-0290254-X
MathSciNet review: 0290254