Journal of the Mathematical Society of Japan

Addendum to: Characterizations of topological dimension by use of normal sequences of finite open covers and Pontrjagin-Schnirelmann theorem

Hisao KATO

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Abstract

In our recent paper [5] in this journal, we have studied strong relations between metrics of spaces and box-counting dimensions by use of Alexandroff-Urysohn metrics d induced by normal sequences. In this addendum, we intend to improve the main theorems given in [5, Theorem 0.1 and 0.2] and give the complete solution for a problem of metrics and two box-counting dimensions.

Article information

Source
J. Math. Soc. Japan Volume 63, Number 3 (2011), 977-983.

Dates
First available: 1 August 2011

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1312203807

Digital Object Identifier
doi:10.2969/jmsj/06330977

Zentralblatt MATH identifier
05950728

Mathematical Reviews number (MathSciNet)
MR2836751

Subjects
Primary: 54F45: Dimension theory [See also 55M10]
Secondary: 28A78: Hausdorff and packing measures 37C45: Dimension theory of dynamical systems 54E35: Metric spaces, metrizability 28A80: Fractals [See also 37Fxx]

Keywords
normal sequence of finite open covers topological dimension lower (upper) box-counting dimensions Menger compacta

Citation

KATO, Hisao. Addendum to: Characterizations of topological dimension by use of normal sequences of finite open covers and Pontrjagin-Schnirelmann theorem. Journal of the Mathematical Society of Japan 63 (2011), no. 3, 977--983. doi:10.2969/jmsj/06330977. http://projecteuclid.org/euclid.jmsj/1312203807.


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References

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