On the dimension of cubic $\mu$-spaces
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- by T. Mizokami PDF
- Proc. Amer. Math. Soc. 82 (1981), 291-298 Request permission
Abstract:
Let $X$ be the countable product of special $\sigma$-metric spaces defined below. Then it is proved that $X \leqslant n$ if and only if there exists a $\sigma$-closure-preserving open base $\mathcal {W}$ for $X$ such that ${\text {Ind}}\;B(W) \leqslant n - 1$ for every $W \in \mathcal {W}$.References
- C. R. Borges and D. J. Lutzer, Characterizations and mappings of $M_{i}$ spaces, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp. 34–40. MR 0362239
- Takemi Mizokami, On Nagata’s problem for paracompact $\sigma$-metric spaces, Topology Appl. 11 (1980), no. 2, 211–221. MR 572375, DOI 10.1016/0166-8641(80)90009-7
- Keiô Nagami, Dimension for $\sigma$-metric spaces, J. Math. Soc. Japan 23 (1971), 123–129. MR 287521, DOI 10.2969/jmsj/02310123
- Keiô Nagami, Perfect class of spaces, Proc. Japan Acad. 48 (1972), 21–24. MR 307207
- Keiô Nagami, The equality of dimensions, Fund. Math. 106 (1980), no. 3, 239–246. MR 584496, DOI 10.4064/fm-106-3-239-246
- Keiô Nagami, Dimension theory, Pure and Applied Mathematics, Vol. 37, Academic Press, New York-London, 1970. With an appendix by Yukihiro Kodama. MR 0271918
- Jun-iti Nagata, On Hyman’s $M$-space, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp. 198–208. MR 0358726
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 291-298
- MSC: Primary 54F45
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609670-4
- MathSciNet review: 609670