## A note on Archimedean Riesz spaces and their extended order duals.(English)Zbl 0612.46007

It is well-known that an Archimedean Riesz space E can be represented as an order dense Riesz subspace of $$C_{\infty}(X)$$, for some Stonian space X. In the present paper it is proved that E is separated by its extended order dual iff X is hyperstonian; moreover, some consequences of this result are considered.

### MSC:

 46A40 Ordered topological linear spaces, vector lattices