Epicomplete Archimedean $l$-groups and vector lattices
نویسندگان
چکیده
منابع مشابه
An equivalence functor between local vector lattices and vector lattices
We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...
متن کاملA Theorem and a Question about Epicomplete Archimedean Lattice-ordered Groups
G always denotes an archimedean `-group. We call G epicomplete if G is divisible, -complete, and laterally -complete. X always denotes a Tychono¤ space. D (X ) is the set of continuous f : X ! [ 1;+1] with f 1 (( 1;+1)) dense. It is familiar and useful that every G has representations in various D (X ) : It is known that (A) G is epicomplete with weak unit e if and only if there is a compact ba...
متن کاملEgoroff, Σ, and Convergence Properties in Some Archimedean Vector Lattices
An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each {an}n∈N ⊆ A there are {λn}n∈N ⊆ (0,∞) and a ∈ A with λnan ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC⇒ RUC): if an ↓ 0 then an → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the formD(X)...
متن کاملInclusions and non-inclusions of Archimedean and Laves lattices
For each pair of graphs from among the Archimedean lattices and their dual Laves lattices we demonstrate that one is a subgraph of the other or prove that neither can be a subgraph of the other. Therefore, we determine the entire partial ordering by inclusion of these 19 infinite periodic graphs. There are a total of 72 inclusion relationships, of which 35 are covering relations in the partial ...
متن کاملSite percolation thresholds and universal formulas for the Archimedean lattices
The site percolation thresholds pc are determined to high precision for eight Archimedean lattices, by the hull-walk gradient-percolation simulation technique, with the results pc = 0.697 043, honeycomb or (6 ), 0.807 904 (3, 12), 0.747 806 (4, 6, 12), 0.729 724 (4, 8), 0.579 498 (3, 6), 0.621 819 (3, 4, 6, 4), 0.550 213 (3, 4), and 0.550 806 (3, 4, 3, 4), and errors of about ±2 × 10. (The rema...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1990-0943603-6