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Non-Archimedean $ C\sp {\char93 }(X)$


Author: Jesús M. Domínguez
Journal: Proc. Amer. Math. Soc. 97 (1986), 525-530
MSC: Primary 54C40; Secondary 46H10, 46P05
DOI: https://doi.org/10.1090/S0002-9939-1986-0840640-1
MathSciNet review: 840640
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Abstract: Let $ E$ be a nonarchimedean rank-one valued field, and $ X$ an ultraregular topological space. We consider the Gelfand subalgebra $ {C^\char93 }(X,E)$ of the algebra of all $ E$-valued continuous functions on $ X$, and the algebra $ F(X,E)$ consisting of those $ E$-valued continuous functions $ f$ for which there exists a compact set $ K \subset X$ such that $ f(X - K)$ is finite. We obtain some characterizations of $ {C^\char93 }(X,E)$, analogous to those obtained in the real case, which we use to find conditions that imply the equality $ {C^\char93 }(X,E) = F(X,E)$ holds.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0840640-1
Keywords: Nonarchimedean valued field, ultraregular space, continuous function algebras, Gelfand subalgebra
Article copyright: © Copyright 1986 American Mathematical Society

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