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Search: MSC category 46E25 ( Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15} )

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Boulabiar, Karim
Characters on $C( X)$
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
Categories:54C30, 46E25

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