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 $M(H^\infty)$

Abstract

We show that the covering dimension, dim E, of the closure E of the interval ]− 1, 1[ in the spectrum of H ∞ equals one. Using Suárez's result that dim M (H ∞ ) = 2, we then compute the Bass and topological stable ranks of the algebra C(M (H ∞ )) sym of real-symmetric continuous functions on M (H ∞ ).