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Proceedings of the American Mathematical Society

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Spaces for which the generalized Cantor space $ 2\sp{J}$ is a remainder


Author: Yusuf Ünlü
Journal: Proc. Amer. Math. Soc. 86 (1982), 673-678
MSC: Primary 54D35; Secondary 54D40
DOI: https://doi.org/10.1090/S0002-9939-1982-0674104-1
MathSciNet review: 674104
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Abstract: Let $ X$ be a locally compact noncompact space, $ m$ be an infinite cardinal and $ \vert J \vert = m$. Let $ F(X)$ be the algebra of continuous functions from $ X$ into $ {\mathbf{R}}$ which have finite range outside of an open set with compact closure and let $ I(X) = \{ g \in F(X):g$ vanishes outside of an open set with compact closure}. Conditions on $ R(X) = F(X)/I(X)$ and internal conditions are obtained which characterize when $ X$ has $ {2^J}$ as a remainder.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0674104-1
Keywords: Compactification, structure space, Freudenthal compactification, Cantor space
Article copyright: © Copyright 1982 American Mathematical Society