Some applications of modular convergence in vector lattice setting

LATTICE-VALUED CATEGORIES OF LATTICE-VALUED CONVERGENCE SPACES

We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

the investigation of research articles in applied linguistics: convergence and divergence in iranian elt context

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Egoroff, 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)...

Some vector valued Siegel modular forms of genus 2

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

Some vector valued Siegel modular forms of genus 3 Eberhard