Hostname: page-component-5c6d5d7d68-tdptf Total loading time: 0 Render date: 2024-09-01T12:13:26.730Z Has data issue: false hasContentIssue false

On a Metric that Characterizes Dimension

Published online by Cambridge University Press:  20 November 2018

J. De Groot*
Affiliation:
Maihematisch Instituut University of Amsterdam
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Sometimes it is possible to characterize topological properties of a metrizable space M by claiming that a certain (topologypreserving) metric ρ can be introduced in M.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Alexandrov, P. and Hopf, H., Topologie (Berlin 1935).Google Scholar
2. de Groot, J. and de Vries, H., A note on non-archimedean metrizations, Indagationes Math., 17(1955), 222224.Google Scholar
3. de Groot, J., Non-archimedian metrics in topology, Proc. Amer. Math. Soc, 7 (1956), 948953.Google Scholar
4. Hurewicz, W., Wallman, H., Dimension Theory (Princeton 1941).Google Scholar
5. Katětov, M., On the dimension of non-separable spaces I, Tsjechoslov. Mat. Zj., 2 (77) (1952), 333368.Google Scholar
6. Morita, K., Normal families and dimension theory for metric spaces, Math. Ann., 128 (1954), 350362.Google Scholar
7. Nagata, J., On a relation between dimension and metrization, Proc. Jap. Ac, 32 (1956), 237240.Google Scholar