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More smoothly real compact spaces

Authors: Andreas Kriegl and Peter W. Michor
Journal: Proc. Amer. Math. Soc. 117 (1993), 467-471
MSC: Primary 46E25; Secondary 46M40, 54D60
MathSciNet review: 1110545
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Abstract: A topological space $ X$ is called $ \mathcal{A}$-real compact if every algebra homomorphism from $ \mathcal{A}$ to the reals is an evaluation at some point of $ X$, where $ \mathcal{A}$ is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. Arias-de-Reyna has shown that any separable Banach space is smoothly real compact. Here we generalize this result to a huge class of locally convex spaces including arbitrary products of separable Fréchet spaces.

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Article copyright: © Copyright 1993 American Mathematical Society

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