Remetrization in Strongly Countabledimensional Spaces
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 748-750
Voir la notice de l'article provenant de la source Cambridge University Press
Although the Lebesgue dimension function is topologically invariant, the dimension-theoretic properties of a metric space can sometimes be made clearer by the introduction of a new, topologically equivalent metric. A considerable amount of effort has been devoted to the problem of constructing such metrics; one example of the fruits of this research is the following theorem by Nagata (2, Theorem 5). In order that dim R ≦ n for a metrizable space R it is necessary and sufficient to be able to define a metric p(x, y) agreeing with the topology of R such that for every ∊ > 0 and for every point x oƒ R, imply A metric ρ which satisfies the condition of this theorem is called Nagata's metric (this term was introduced, to the best of the author's knowledge, by Nagami (1, Definition 9.3)).
Wenner, B. R. Remetrization in Strongly Countabledimensional Spaces. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 748-750. doi: 10.4153/CJM-1969-084-4
@article{10_4153_CJM_1969_084_4,
author = {Wenner, B. R.},
title = {Remetrization in {Strongly} {Countabledimensional} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {748--750},
year = {1969},
volume = {21},
number = {1},
doi = {10.4153/CJM-1969-084-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-084-4/}
}
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[3] 3. Wenner, B. R., Dimension on boundaries of e-spheres, Pacific J. Math. 27 (1968), 201—210. Google Scholar
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