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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Extending continuous functions in zero-dimensional spaces
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by Nancy M. Warren PDF
Proc. Amer. Math. Soc. 52 (1975), 414-416 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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