An inequality concerning three fundamental dimensions of paracompact -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

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that Ind for any nonempty paracompact -space.

**[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**-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**, https://doi.org/10.2969/jmsj/01820158

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0630056-0

Keywords:
-space,
covering dimension,
large inductive dimension,
small inductive dimension

Article copyright:
© Copyright 1981
American Mathematical Society