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Metrizability of general ANR


Author: Kōichi Tsuda
Journal: Proc. Amer. Math. Soc. 96 (1986), 375-378
MSC: Primary 54C55; Secondary 54B35, 54D18, 54F15, 54F45
DOI: https://doi.org/10.1090/S0002-9939-1986-0818475-5
MathSciNet review: 818475
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Abstract: We show that every nonmetrizable $ {\text{ANR(}}\mathcal{P}{\text{)}}$ contains a copy of a Tychonoff cube of uncountable weight. Hence, every finite dimensional $ {\text{ANR(}}\mathcal{P}{\text{)}}$ is metrizable, and every $ {\text{ANR(}}\mathcal{P}{\text{)}}$, each point of which is a $ {G_\delta }$-set, is metrizable, where $ \mathcal{P}$ denotes the class of all paracompact $ p$-spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0818475-5
Keywords: ANR, paracompact $ p$-space, generalized Peano continuum
Article copyright: © Copyright 1986 American Mathematical Society

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