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

Filter, Wolfgang

Libertas Math. 6, 101-106 (1986).

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

Keywords:

hypercomplete Riesz space; Archimedean Riesz space; Stonian space; extended order dual; hyperstonian