The First Cohomology Group of a Maximal Ideal Space
Given Banach algebras 𝔄1 and 𝔄2 with maximal ideal spaces ℳ 1 and ℳ 2, if 𝔄1 and 𝔄2 are isomorphic as algebras, then ℳ 1 and ℳ 2 are homeomorphic. It is thus to be expected that the topology of ℳ (𝔄) is reflected in the algebraic structure of 𝔄, for an arbitrary Banach algebra 𝔄.
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