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September 2008 Complementability of spaces of affine continuous functions on simplices
Miroslav Bačák, Jiří Spurný
Bull. Belg. Math. Soc. Simon Stevin 15(3): 465-472 (September 2008). DOI: 10.36045/bbms/1222783093

Abstract

We construct metrizable simplices $X_1$ and $X_2$ and a homeomorphism $\varphi:\overline{ext X_1}\to\overline{ext X_2}$ such that $\varphi(ext X_1)=ext X_2$, the space $\mathfrak{A}(X_1)$ of all affine continuous functions on $X_1$ is complemented in $\mathcal C(X_1)$ and $\mathfrak{A}(X_2)$ is not complemented in any $\mathcal C(K)$ space. This shows that complementability of the space $\mathfrak{A}(X)$ cannot be determined by topological properties of the couple $(ext X,\overline{ext X})$.

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Miroslav Bačák. Jiří Spurný. "Complementability of spaces of affine continuous functions on simplices." Bull. Belg. Math. Soc. Simon Stevin 15 (3) 465 - 472, September 2008. https://doi.org/10.36045/bbms/1222783093

Information

Published: September 2008
First available in Project Euclid: 30 September 2008

zbMATH: 1159.46005
MathSciNet: MR2457962
Digital Object Identifier: 10.36045/bbms/1222783093

Subjects:
Primary: 46A55
Secondary: 46B03

Rights: Copyright © 2008 The Belgian Mathematical Society

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Vol.15 • No. 3 • September 2008
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