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Proceedings of the American Mathematical Society

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

 

 

Continuous mappings from Cantor spaces onto inverse limit spectra


Author: Alan H. Schoenfeld
Journal: Proc. Amer. Math. Soc. 60 (1976), 331-334
MSC: Primary 54B25; Secondary 54C05
DOI: https://doi.org/10.1090/S0002-9939-1976-0420537-5
MathSciNet review: 0420537
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Abstract: Let $ \mathcal{S} = \{ {X_\alpha };{f_{\alpha \beta }}:{X_\beta } \to {X_\alpha }\} $ be an inverse limit spectrum of compact Hausdorff spaces. We obtain necessary and sufficient conditions that there be a closed subspace W of a Cantor space and a family $ \{ {f_\alpha }:W \to {X_\alpha }\} $ of continuous surjections such that for each pair $ \alpha < \beta ,{f_{\alpha \beta }} \circ {f_\beta } = {f_\alpha }$. This result is applied to a special class of inverse spectra.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0420537-5
Keywords: Inverse limit spectra, Cantor spaces, continuous surjections
Article copyright: © Copyright 1976 American Mathematical Society