2024/04/26 by Anthony W. Hager, Brian Wynne, Hager, Anthony W. +1
Computer Science · Mathematics · #06F20 #46A40 #54D35 #54H10 #Advanced Algebra and Logic #Approximation Theory and Sequence Spaces #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2404.17628
openalex publication_date 2024/04/26 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28
The property of a vector lattice of sufficiently many projections (SMP) is informed by restricting attention to archimedean A with a distinguished weak order unit u (the class, or category, \bfW), where the Yosida representation A ≤ D(Y(A,u)) is available. Here, A SMP is equivalent to Y(A,u) having a π-base of clopen sets of a certain type called ``local". If the unit is strong, all clopen sets are local and A is SMP if and only if Y(A,u) has clopen π-base, a property we call π-zero-dimensional (πZD). The paper is in two parts: the first explicates the similarities of SMP and πZD; the second consists of examples, including πZD but not SMP, and constructions of many SMP's which seem scarce in the literature.