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Characters on $C( X)$

  • Karim Boulabiar,
    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
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Abstract

The precise condition on a completely regular space $X$ for every character on $C(X) $ to be an evaluation at some point in $X$ is that $X$ be realcompact. Usually, this classical result is obtained relying heavily on involved (and even nonconstructive) extension arguments. This note provides a direct proof that is accessible to a large audience.
Keywords: characters, realcompact, evaluation, real-valued continuous functions characters, realcompact, evaluation, real-valued continuous functions
MSC Classifications: 54C30, 46E25 show english descriptions Real-valued functions [See also 26-XX]
Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}
54C30 - Real-valued functions [See also 26-XX]
46E25 - Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}
 

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