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Equivalence of Lipschitz Structures

Published online by Cambridge University Press:  20 November 2018

Robert B. Fraser Jr.
Robert B. Fraser Jr.*
Affiliation:
Louisiana State University, Baton Rouge
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In 1962, V. Ju. Sandberg gave a definition of a Lipschitz structure more general than that of a metric space. In [1], the author gave alternate definitions of a Lipschitz structure, one in terms of a family of pseudometrics and the other in terms of sequences of entourages. These definitions were proved equivalent to each other. In 1965, Sandberg gave conditions under which his Lipschitz structure was generated by a metric.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 363 - 368
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Fraser, R. B., Axiom systems for Lipschitz structures, Fund. Math., 64 (1969), 15-24.Google Scholar
2. Gaal, S. A., Point Set Topology, Academic Press, New York, (1964), 164-165.Google Scholar
3. Sandberg, V. Ju., On Lipschitz spaces, Dokl. Akad. Nauk SSSR, 145(1962), p. 284.Google Scholar
4. Sandberg, V. Ju., The metrization of Lipschitz spaces, Dokl. Akad. Nauk SSSR, 155(1964), 1018-1021.Google Scholar