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An inequality concerning three fundamental dimensions of paracompact $ \sigma $-spaces


Author: Shinpei Oka
Journal: Proc. Amer. Math. Soc. 83 (1981), 790-792
MSC: Primary 54F45; Secondary 54E18
MathSciNet review: 630056
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Abstract: It is shown that Ind $ {\text{Ind}}X \leqslant \dim X + {\text{ind}}X $ for any nonempty paracompact $ \sigma $-space.


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  • [1] Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 0188982
  • [2] Ryszard Engelking, Dimension theory, North-Holland Publishing Co., Amsterdam-Oxford-New York; PWN—Polish Scientific Publishers, Warsaw, 1978. Translated from the Polish and revised by the author; North-Holland Mathematical Library, 19. MR 0482697
  • [3] I. M. Leibo, On the equality of dimensions for closed images of metric spaces, Soviet Math. Dokl. 15 (1974), 835-839.
  • [4] -, On closed images of metric spaces, Soviet Math. Dokl. 16 (1975), 1292-1295.
  • [5] Shinpei Oka, Dimension of finite unions of metric spaces, Math. Japon. 24 (1979/80), no. 4, 351–362. MR 557465
  • [6] -, A generalization of free $ L$-spaces, Tsukuba J. Math, (to appear).
  • [7] 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 0230283
  • [8] B. A. Pasynkov, On the spectral decomosition of topological spaces, Mat. Sb. (N.S.) 66 (108) (1965), 35–79 (Russian). MR 0172236
  • [9] V. V. Filippov, On bicompacta with noncoinciding inductive dimensions, Soviet Math. Dokl. 11 (1970), 635-638.
  • [10] Keiô Nagami, A normal space 𝑍 with 𝑖𝑛𝑑𝑍=0, 𝑑𝑖𝑚𝑍=1, 𝐼𝑛𝑑𝑍=2, J. Math. Soc. Japan 18 (1966), 158–165. MR 0199842

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0630056-0
Keywords: $ \sigma $-space, covering dimension, large inductive dimension, small inductive dimension
Article copyright: © Copyright 1981 American Mathematical Society