Tokyo Journal of Mathematics

Higher Dimensional Compacta with Algebraically Closed Function Algebras


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For a compact Hausdorff space $X$, $C(X)$ denotes the ring of all complex-valued continuous functions on $X$. We say that $C(X)$ is \textit{algebraically closed} if every monic algebraic equation with $C(X)$-coefficients has a root in $C(X)$. Modifying the construction of [2], we show that, for each $m = 1,2, \cdots, \infty$, there exists an $m$-dimensional compact Hausdorff space $X(m)$ such that $C(X(m))$ is algebraically closed.

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Tokyo J. Math., Volume 32, Number 2 (2009), 441-445.

First available in Project Euclid: 22 January 2010

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Zentralblatt MATH identifier

Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 54F65: Topological characterizations of particular spaces


KAWAMURA, Kazuhiro. Higher Dimensional Compacta with Algebraically Closed Function Algebras. Tokyo J. Math. 32 (2009), no. 2, 441--445. doi:10.3836/tjm/1264170242.

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