Abstract. Let X and Y be compact Hausdorff spaces, E be a Banach lattice and F be an AM space with unit. Let π : C(X, E) → C(Y, F ) be a Riesz isomorphism such that 0 ∈ f (X) if and only if 0 ∈ π(f )(Y ) for each f ∈ C(X, E). We prove that X is homeomorphic to Y and E is Riesz isomorphic to F . This generalizes some known results.

Abstract. V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E p 0 a  E q I b where 1 % pY q`I , p j q, a a n I n 1 and b b n I n 1 are sequences of positive numbers and E p 0 a , E q I b are respectively p -finite and q -infinite type power series spaces.

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Abstract. Let X be a real compact space. Without using the axiom of choice we present a simple and direct proof that a non-zero homomorphism on C(X) is determined by a point.