Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1981-0630056-0
MathSciNet review: 630056
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that Ind $ {\text{Ind}}X \leqslant \dim X + {\text{ind}}X $ for any nonempty paracompact $ \sigma $-space.


References [Enhancements On Off] (What's this?)

  • [1] C. J. R. Borges, On stratifiable spaces, Facific J. Math. 17 (1966), 1-16. MR 0188982 (32:6409)
  • [2] R. Engelking, Dimension theory, North-Holland, Amsterdam, 1978. MR 0482697 (58:2753b)
  • [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] S. Oka, Dimension of finite unions of metric spaces, Math. Japon. 24 (1979), 351-362. MR 557465 (81d:54028)
  • [6] -, A generalization of free $ L$-spaces, Tsukuba J. Math, (to appear).
  • [7] A. Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 9 (1967), 236-254. MR 0230283 (37:5846)
  • [8] B. A. Pasynkov, On the spectral decomposition of topological spaces, Amer. Math. Soc. Transl. (2) 73 (1966), 83-134. MR 0172236 (30:2456)
  • [9] V. V. Filippov, On bicompacta with noncoinciding inductive dimensions, Soviet Math. Dokl. 11 (1970), 635-638.
  • [10] K. Nagami, A normal space $ Z$ with $ {\text{ind }}Z = 0$, $ \dim Z = 1$, $ {\text{Ind }}Z = 2$, J. Math. Soc. Japan 18 (1966), 158-165. MR 0199842 (33:7982)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F45, 54E18

Retrieve articles in all journals with MSC: 54F45, 54E18


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

American Mathematical Society