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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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Keywords: Zero-dimensional space, <!– MATH ${C^{\ast }}$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^{\ast }}$">-embedded
Article copyright: © Copyright 1975 American Mathematical Society