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A Characterization of the Topological Dimension

Published online by Cambridge University Press:  20 November 2018

Gerd Rodé
Gerd Rodé*
Affiliation:
Department of Mathematics, University of California, Santa Barbara California 93106and H.-Loens-Str. 27 6602, Saarbruecken West Germany
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Abstract

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This paper gives a new characterization of the dimension of a normal Hausdorff space, which joins together the Eilenberg-Otto characterization and the characterization by finite coverings. The link is furnished by the notion of a system of faces of a certain type (N1,..., NK), where N1,..., NK, K are natural numbers. It is shown that a space X contains a system of faces of type (N1,..., NK) if and only if dim(X) ≥ N1 + … + NK. The two limit cases of the theorem, namely Nk = 1 for 1 ≤ k ≤ K on the one hand, and K = 1 on the other hand, give the two known results mentioned above.

Keywords

54F45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 487 - 490
Copyright
Copyright © Canadian Mathematical Society 1982

References

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4. Nagata, J., Modern Dimension Theory. Interscience, New York 1965.Google Scholar