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

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 Suárezʼs result that , we then compute the Bass and topological stable ranks of the algebra C(M(H∞))sym of real-symmetric continuous functions on M(H∞).