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We present a constructive proof of the Stone-Yosida representation theoremfor Riesz spaces motivated by considerations from formal topology. This theoremis used to derive a representation theorem for f-algebras. In turn, thistheorem implies the Gelfand representation theorem for C*-algebras of operatorson Hilbert spaces as formulated by Bishop and Bridges. Our proof is shorter,clearer, and we avoid the use of approximate eigenvalues.

Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems