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~∞)

摘要

We show that the covering dimension, dim E, of the closure £ of the interval | -1.1| in the spectrum of H~∞ equals one. Using Suarez'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~∞).