Equivalence of Lipschitz Structures
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 363-368
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Jr., Robert B. Fraser. Equivalence of Lipschitz Structures. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 363-368. doi: 10.4153/CMB-1972-066-4
@article{10_4153_CMB_1972_066_4,
author = {Jr., Robert B. Fraser},
title = {Equivalence of {Lipschitz} {Structures}},
journal = {Canadian mathematical bulletin},
pages = {363--368},
year = {1972},
volume = {15},
number = {3},
doi = {10.4153/CMB-1972-066-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-066-4/}
}
[1] 1. Fraser, R. B., Axiom systems for Lipschitz structures, Fund. Math., 64 (1969), 15-24. Google Scholar
[2] 2. Gaal, S. A., Point Set Topology, Academic Press, New York, (1964), 164-165. Google Scholar
[3] 3. Sandberg, V. Ju., On Lipschitz spaces, Dokl. Akad. Nauk SSSR, 145(1962), p. 284. Google Scholar
[4] 4. Sandberg, V. Ju., The metrization of Lipschitz spaces, Dokl. Akad. Nauk SSSR, 155(1964), 1018-1021. Google Scholar
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