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A new proof of the Banach-stone theorem

Published online by Cambridge University Press:  17 April 2009

N.J. Cutland  and
G.B. Zimmer
N.J. Cutland
Affiliation:
Department of MathematicsUniversity of HullHull HU6 7RXEngland
G.B. Zimmer
Affiliation:
Division of Science and MathematicsMississippi University for WomenColumbus MS 39701United States of America
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Abstract

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Banach's original proof of the Banach-Stone theorem for compact metric spaces uses peak functions, that is, continuous functions which assume their norm in just one point. We show by using nonstandard methods that the peak point approach also works for compact Hausdorff spaces. The peak functions are replaced by internal functions whose standard part is supported in one monad.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 55 - 58
Copyright
Copyright © Australian Mathematical Society 1998

References

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