Let

${X}_{1}$ and

${X}_{2}$ be compact Hausdorff spaces and let

$C\left({X}_{i}\right)$ (

$i=1,2$) denote the space of real-valued continuous functions on

${X}_{i}$ equipped with supremum norm. The deduction of topological affinities between the spaces

${X}_{1}$ and

${X}_{2}$ from certain algebraic or geometric relations between

$C\left({X}_{1}\right)$ and

$C\left({X}_{2}\right)$ has been widely treated in the literature, being the Banach-Stone theorem the first and most inspiring result. The authors deal with this type of questions for spaces of continuous functions that take values in a Banach lattice. Among others, their main result is the following: let

${X}_{1}$,

${X}_{2}$ be compact Hausdorff spaces and let

$E$ be a Banach lattice. Suppose there is a Riesz isomorphism

${\Phi}:C({X}_{1},E)\u27f6C({X}_{2},\mathbb{R})$ such that

$\phi \left(f\right)$ has no zeros if

$f$ has none. Then

${X}_{1}$ and

${X}_{2}$ are homeomorphic and

$E$ and

$\mathbb{R}$ are Riesz isomorphic.