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Characters on C(X)

Published online by Cambridge University Press:  20 November 2018

Karim Boulabiar
Karim Boulabiar*
Affiliation:
Research Laboratory of Algebra, Topology, Arithmetic, and Order, Faculty of Mathematical, Physical and Natural Sciences of Tunis, Tunis-El Manar University, 2092-El Manar, Tunisia. e-mail: [email protected]
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Abstract

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The precise condition on a completely regular space $X$ for every character on $C\left( X \right)$ to be an evaluation at some point in $X$ is that $X$ be realcompact. Usually, this classical result is obtained by relying heavily on involved (and even nonconstructive) extension arguments. This note provides a direct proof that is accessible to a large audience.

Keywords

54C3046E25charactersrealcompactevaluationreal-valued continuous functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 7 - 8
Copyright
Copyright © Canadian Mathematical Society 2015

References

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