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Proceedings of the American Mathematical Society

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

 

 

Extending continuous functions in zero-dimensional spaces


Author: Nancy M. Warren
Journal: Proc. Amer. Math. Soc. 52 (1975), 414-416
MSC: Primary 54C45
DOI: https://doi.org/10.1090/S0002-9939-1975-0383340-X
MathSciNet review: 0383340
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Abstract: Suppose that $ X$ is a completely regular, zero-dimensional space and that a dense subset $ S$ of $ X$ is not $ {C^{\ast}}$-embedded in $ X$; does there then exist a two-valued function in $ {C^{\ast}}(S)$ with no continuous extension to $ X$? The answer is negative even if $ X$ is a compact space. The question was raised by N. J. Fine and L. Gillman in Extension of continuous functions in $ \beta N$, Bull. Amer. Math. Soc. 66 (1960), 376-381.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0383340-X
Keywords: Zero-dimensional space, $ {C^{\ast}}$-embedded
Article copyright: © Copyright 1975 American Mathematical Society