## 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

#### 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 in Project Euclid: 1 August 2011

http://projecteuclid.org/euclid.jmsj/1312203807

Digital Object Identifier
doi:10.2969/jmsj/06330977

Mathematical Reviews number (MathSciNet)
MR2836751

Zentralblatt MATH identifier
1251.54031

#### Citation

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

#### References

• R. D. Anderson, One-dimensional continuous curves and a homogeneity theorem, Ann. of Math. (2), 68 (1958), 1–16.
• T. Banakh and M. Tuncali, Controlled Hahn-Mazurkiewicz Theorem and some new dimension functions of Peano continua, Topology and its Applications, 154 (2007), 1286–1297.
• M. Bestvina, Characterizing $k$-dimensional universal Menger compacta, Mem. Amer. Math. Soc., 71 (1988), no.,380.
• W. Hurewicz and H. Wallman, Dimension Theory, Princeton Univ. Press, Princeton, New Jersey, 1948.
• H. Kato and M. Matsumoto, Characterizations of topological dimension by use of normal sequences of finite open covers and Pontrjagin-Schnirelmann theorem, J. Math. Soc. Japan, to appear.
• K. Nagami, Dimension Theory, Academic Press, New York-London, 1970.
• J. Nagata, Modern Dimension Theory, Heldermann Verlag, 1983.
• J. Nagata, Modern General Topology, North-Holland, Amsterdam, 1985.
• J. Nagata, Open problems left in my wake of research, Topology and its Applications, 146/147 (2005), 5–13.
• L. Pontrjagin and L. Schnirelmann, Sur une propriété métrique de la dimension, Ann. of Math. (2), 33 (1932), 156–162.