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Proceedings of the American Mathematical Society

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

 
 

 

Spaces of AANRs


Author: Zvonko Čerin
Journal: Proc. Amer. Math. Soc. 83 (1981), 609-615
MSC: Primary 54B20; Secondary 54C15, 54C55, 54E52
DOI: https://doi.org/10.1090/S0002-9939-1981-0627704-8
MathSciNet review: 627704
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Abstract: For a metric space $ X$, let $ {\text{AAN}}{{\text{R}}_{\text{C}}}(X)$ denote the hyperspace of all nonempty approximative absolute neighborhood retracts in the sense of Clapp in $ X$ topologized with the metric of continuity. We show that $ {\text{AAN}}{{\text{R}}_{\text{C}}}(X)$ is topologically complete iff $ X$ is topologically complete. Some subsets of the first Baire category in $ {\text{AAN}}{{\text{R}}_{\text{C}}}(X)$ for a $ Q$-manifold $ X$ are identified. For example, the collection $ {\text{AAN}}{{\text{R}}_{\text{N}}}(X)$ of all nonempty approximative absolute neighborhood retracts in the sense of Noguchi in $ X$ is such a subset.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627704-8
Keywords: Approximative absolute neighborhood retract, metric of continuity, topologically complete, $ Q$-manifold
Article copyright: © Copyright 1981 American Mathematical Society

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