1. Truncated vector lattices: A Maeda-Ogasawara type representation.
- Author
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Boulabiar, Karim and Hajji, Rawaa
- Subjects
- *
RIESZ spaces , *COMMERCIAL space ventures , *HAUSDORFF spaces , *CHARACTERISTIC functions , *COMPACT spaces (Topology) - Abstract
Let L be a truncated Archimedean vector lattice whose truncation is denoted by *. In a recent paper, we proved that there exists a locally compact Hausdorff space X such that L is a lattice isomorphic with a truncated vector lattice of functions in C∞(X) whose truncation is provided by meet with some characteristic function on X. This representation, no matter how interesting it is, has a major drawback, namely, C∞(X) need not be a vector lattice, unless X is extremally disconnected. The main purpose of this paper is to remedy this shortcoming by proving that, indeed, an extremally disconnected locally compact space X can be found such that L can be seen as an order dense vector sublattice of C∞(X) whose truncation is provided, again, by meet with some characteristic function on X. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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