Čech Cohomology and Covering Dimension for the H^∞ Maximal Ideal Space

Abstract

It is proved that the n-Čech cohomology groups of the H^∞ maximal ideal space (X(H^∞)) are trivial for n ≥ 2, and that single elements of H^∞ separate points from closed sets in X(H^∞). These results are used to prove that the covering dimension of X(H^∞) is 2.