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December 2009 Higher Dimensional Compacta with Algebraically Closed Function Algebras
Tokyo J. Math. 32(2): 441-445 (December 2009). DOI: 10.3836/tjm/1264170242


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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Kazuhiro KAWAMURA. "Higher Dimensional Compacta with Algebraically Closed Function Algebras." Tokyo J. Math. 32 (2) 441 - 445, December 2009.


Published: December 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1197.54044
MathSciNet: MR2589955
Digital Object Identifier: 10.3836/tjm/1264170242

Primary: 46J10
Secondary: 54F65

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

Vol.32 • No. 2 • December 2009
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