Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4672815 | Indagationes Mathematicae | 2016 | 10 Pages |
Abstract
A surjective homomorphism Aâ ÏB of Riesz spaces (real vector lattices) has the “countable lifting property” CLP if: For each countable pairwise disjoint {bn} in B, there are disjoint{an} in A with Ï(an)=bn for each n. Previous thoughts on this are due to Topping (1965), Conrad (1968), and in considerable depth, Moore (1970), (and little subsequent, to our knowledge). Here, we consider the issue mostly (not entirely) for Riesz spaces resembling C(X)'s. We show (inter alia): Aâ ÏB will have CLP if (a) B is laterally Ï-complete; or if (b) B=C(Y) for Y locally compact and Ï-compact; or if (c) A is an f-algebra with identity, which is archimedean and uniformly complete, and B is (merely) archimedean (e.g., A=C(X) and B=C(Y), for any X, Y). The main technical device is the notion: b is a weak supremum of {bn} if b=âλnbn for some {λn}â(0,+â).
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Anthony W. Hager, Robert Raphael,