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Spaces Of Dimension Zero

Published online by Cambridge University Press:  20 November 2018

Bernhard Banaschewski
Bernhard Banaschewski*
Affiliation:
Hamilton College, McMaster University, Hamilton, Ontario
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1. Introduction. In a recent paper (1) it was remarked that the theory of zero-dimensional spaces is exactly that part of general topology which can be described in terms of equivalence relations. Here, it will be shown how this idea can be used to obtain the following characterizations of certain types of zero-dimensional spaces:

Any compact zero-dimensional space which has a denumerable basis for its open sets and is dense in itself is homeomorphic to the space of 2-adic integers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 38 - 46
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Banaschewski, B., Ueber nulldimensionale Räume, Math. Nachr. 13 (1955), 129–140.Google Scholar
2. Birkhoff, G., Lattice theory, Amer. Math. Soc. Coll. Publ. XXV (1948).Google Scholar
3. Bourbaki, N., Topologie gén้rale, chaps. I and II, Act. sci. et ind. (Paris, 1948).Google Scholar
4. Deuring, M., Algebren (Berlin, 1935).Google Scholar
5. Fox, G. E. N., The topology of p-adic number fields, doctoral thesis, McGill University, 1955.Google Scholar
6. Kuratowski, C., Topologie I and II, Monogralie Matematvczne, XX and XXI (Warsaw, 1948 and 1950).Google Scholar