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Sums of finite-dimensional spaces

Published online by Cambridge University Press:  17 April 2009

B.R. Wenner
B.R. Wenner
Affiliation:
University of Missouri-Kansas City, Kansas City, Missouri.
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Abstract

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Analogues are developed to the sum theorems in the dimension theory of metric spaces. It is shown that, within the class of metric spaces, any locally countable, σ-locally finite, or closure-preserving sum of finite-dimensional sets is countable-dimensional. Similar results are obtained under the more general hypothesis of countable-dimensional rather than finite-dimensional sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 357 - 361
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Nagata, J., ‘On the countable sum of zero-dimensional spaces’, Fund. Math. 48 (1960), 1–14.CrossRefGoogle Scholar
[2]Nagata, Jun-iti, Modern dimension theory (John Wiley, New York, 1965).Google Scholar