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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An inequality concerning three fundamental dimensions of paracompact $\sigma$-spaces
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by Shinpei Oka PDF
Proc. Amer. Math. Soc. 83 (1981), 790-792 Request permission

Abstract:

It is shown that Ind ${\text {Ind}}X \leqslant \dim X + {\text {ind}}X$ for any nonempty paracompact $\sigma$-space.
References
  • Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982, DOI 10.2140/pjm.1966.17.1
  • Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], PaΕ„stwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
  • I. M. Leǐbo, On the equality of dimensions for closed images of metric spaces, Soviet Math. Dokl. 15 (1974), 835-839. β€”, On closed images of metric spaces, Soviet Math. Dokl. 16 (1975), 1292-1295.
  • Shinpei Oka, Dimension of finite unions of metric spaces, Math. Japon. 24 (1979/80), no.Β 4, 351–362. MR 557465
  • β€”, A generalization of free $L$-spaces, Tsukuba J. Math, (to appear).
  • Akihiro Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 9 (1968), 236–254 (1968). MR 230283
  • B. A. Pasynkov, On the spectral decomosition of topological spaces, Mat. Sb. (N.S.) 66 (108) (1965), 35–79 (Russian). MR 0172236
  • V. V. Filippov, On bicompacta with noncoinciding inductive dimensions, Soviet Math. Dokl. 11 (1970), 635-638.
  • KeiΓ΄ Nagami, A normal space $Z$ with $\textrm {ind}\,Z=0$, $\textrm {dim}\, Z=1$, $\textrm {Ind}\,Z=2$, J. Math. Soc. Japan 18 (1966), 158–165. MR 199842, DOI 10.2969/jmsj/01820158
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 790-792
  • MSC: Primary 54F45; Secondary 54E18
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0630056-0
  • MathSciNet review: 630056