Semi unbounded order convergent in ordered vector spaces

2021/12/31 by Ebrahimzadeh, Masoumeh, Azar, Kazem Haghnejad
#46B40 #46B42 #47B65 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2112.15585

Abstract

Let X be an ordered vector space. The net \x_α\⊆ X is semi unbounded order convergent to x (in symbol x_α\xrightarrowsuox), if there is a net \y_β\, possibly over a different index set, such that y_β\downarrow 0 and for every β there exists α₀ such that \\±(x_α- x)\^u,y\^l⊆ \y_β\^l, whenever α≥ α₀ and for all 0≤ y ∈ X. In vector lattice E, semi unbounded order convergence is equivalent with unbounded order convergence. We study some properties of this convergence and some of its relationships with others known order convergence.

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