Non-Archimedean 𝐶^{#}(𝑋)

Domínguez, Jesús M.

doi:10.1090/S0002-9939-1986-0840640-1

Non-Archimedean $C^ {\#}(X)$
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Proc. Amer. Math. Soc. 97 (1986), 525-530 Request permission

Abstract:

Let $E$ be a nonarchimedean rank-one valued field, and $X$ an ultraregular topological space. We consider the Gelfand subalgebra ${C^\# }(X,E)$ 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 ${C^\# }(X,E)$, analogous to those obtained in the real case, which we use to find conditions that imply the equality ${C^\# }(X,E) = F(X,E)$ holds.

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