A Dauns-Hofmann theorem for TAF-algebras

Let A be a TAF-algebra, Z(A) the centre of A, Id(A) the ideal lattice of A, and Mir(A) the space of meet-irreducible elements of Id(A), equipped with the hull-kernel topology. It is shown that Mir(A) is a compact, locally com pact, second countable, T-0-space, that Id(A) is an algebraic lattice isomo rphic to the lattice of open subsets of Mir(A), and that Z(A) is isomorphic to the algebra of continuous, complex functions on Mir(A). If A is semisim ple, then Z(A) is isomorphic to the algebra of continuous, complex function s on Prim(A), the primitive ideal space of A. If A is strongly maximal, the n the sum of two closed ideals of A is closed.