Paper detail

Semi unbounded order convergent in ordered vector spaces

Let $X$ be an ordered vector space. The net $\{x_α\}\subseteq X$ is semi unbounded order convergent to $x$ (in symbol $x_α\xrightarrow{suo}x$), 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 $α_0$ such that $\{\{\pm(x_α- x)\}^u,y\}^l\subseteq \{y_β\}^l$, whenever $α\geq α_0$ and for all $0\leq y \in X$. 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.