The statistically unbounded τ -convergence on locally solid Riesz spaces

Abstract

A sequence $(x_n)$ in a locally solid Riesz space (E, τ ) is said to be statistically unbounded τ -convergent tox ∈ E if, for every zero neighborhood U , 1/n I {k ≤ n : |xk − x| ∧ u /∈ U}I → 0 as n → ∞In this paper, we introduce theconcept of the st-uτ -convergence and give the notions of st-uτ -closed subset, st-uτ -Cauchy sequence, st-uτ -continuousand st-uτ -complete locally solid vector lattice. Also, we give some relations between the order convergence and thest-uτ -convergence.