Proceedings of the American Mathematical Society

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A note on cohomological dimension of approximate movable spaces


Author: Tadashi Watanabe
Journal: Proc. Amer. Math. Soc. 123 (1995), 2883-2885
MSC: Primary 54C55; Secondary 54C56, 54F45
MathSciNet review: 1327050
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Abstract: We show that any approximate movable compact metric space X satisfies the equality $ \dim X = {\dim _\mathbb{Z}}X$ without finite dimensional condition. Thus there is no approximate movable compact metric space X with $ \dim X = \infty $ and $ {\dim _\mathbb{Z}}X < \infty $. Since ANRs and some generalized ANRs are approximate movable, they satisfy the above equality.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1327050-3
Keywords: Covering dimension, cohomological dimension, ANR, generalized ANR, approximate movability
Article copyright: © Copyright 1995 American Mathematical Society