Y. A. Dabboorasad
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View article: $um$-Topology in multi-normed vector lattices
$um$-Topology in multi-normed vector lattices Open
Let $\mathcal{M}=\{m_λ\}_{λ\inΛ}$ be a separating family of lattice seminorms on a vector lattice $X$, then $(X,\mathcal{M})$ is called a multi-normed vector lattice (or MNVL). We write $x_α\xrightarrow{\mathrm{m}} x$ if $m_λ(x_α-x)\to 0$ …
View article: \MakeLowercase{$um$}-Topology in Multi-Normed Vector Lattices
\MakeLowercase{$um$}-Topology in Multi-Normed Vector Lattices Open
Let $\mathcal{M}=\{m_\lambda\}_{\lambda\in\Lambda}$ be a separating family of lattice seminorms on a vector lattice $X$, then $(X,\mathcal{M})$ is called a multi-normed vector lattice (or MNVL). We write $x_\alpha \xrightarrow{\mathrm{m}} …
View article: $u\tau$-Convergence in locally solid vector lattices
$u\tau$-Convergence in locally solid vector lattices Open
Let $x_\\alpha$ be a net in a locally solid vector lattice $(X,\\tau)$; we say\nthat $x_\\alpha$ is unbounded $\\tau$-convergent to a vector $x\\in X$ if $\\lvert\nx_\\alpha-x \\rvert\\wedge w \\xrightarrow{\\tau} 0$ for all $w\\in X_+$. I…
View article: $uτ$-Convergence in locally solid vector lattices
$uτ$-Convergence in locally solid vector lattices Open
Let $x_α$ be a net in a locally solid vector lattice $(X,τ)$; we say that $x_α$ is unbounded $τ$-convergent to a vector $x\in X$ if $\lvert x_α-x \rvert\wedge w \xrightarrowτ 0$ for all $w\in X_+$. In this paper, we study general propertie…
View article: Unbounded $ \tau $-Convergence in locally solid Riesz spaces
Unbounded $ \tau $-Convergence in locally solid Riesz spaces Open
Let $(X,\tau)$ be a locally solid Riesz space and $x_\alpha$ be a net in $X$, we say that $x_\alpha$ is unbounded $\tau$-convergent to a vector $x\in X$ if $\lvert x_\alpha-x\rvert\wedge w \xrightarrow{\tau} 0$ for all $w \in X_+$. In this…
View article: Order convergence in infinite-dimensional vector lattices is not topological
Order convergence in infinite-dimensional vector lattices is not topological Open
In this note, we show that the order convergence in a vector lattice $X$ is not topological unless $\dim X