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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
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