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arXiv · 1602.06841

The covering dimension of a distinguished subset of the spectrum $M(H^\infty)$ of $H^\infty$ and the algebra of real-symmetric and continuous functions on $M(H^\infty)$

Raymond Mortini
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Abstract

We show that the covering dimension, $\dim E$, of the closure $E$ of the interval $]-1,1[$ in the spectrum of $H^\infty$ equals one. Using Su\'arez's result that $\dim M(H^\infty)=2$, we then compute the Bass and topological stable ranks of the algebra $C(M(H^\infty))_{\rm\scriptscriptstyle sym}$ of real-symmetric continuous functions on $M(H^\infty)$.

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Raymond Mortini. 2016-02-17. The covering dimension of a distinguished subset of the spectrum $M(H^\infty)$ of $H^\infty$ and the algebra of real-symmetric and continuous functions on $M(H^\infty)$. https://doi.org/10.1016/j.topol.2011.12.005

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