Truncated vector lattices: A Maeda-Ogasawara type representation

1AbstractLet 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.Mathematics Subject Classification (2020): 06F2046E0546A4054C30Key words: Boolean algebraextended-real valued functionextremally disconnectedHausdorffhull-kernel topologylocally compactmulti-truncationprime idealtruncationtruncated vector latticepolarrepresentationweak truncation