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Sums of finite-dimensional spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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