Semi unbounded order convergent in ordered vector spaces

Abstract

Let $X$ be an ordered vector space. The net $\{x_{\alpha }\}\subseteq X$ is semi unbounded order convergent to $x$ (in symbol $x_{\alpha }\stackrel{suo}{\to }x$), if there is a net $\{y_{\beta }\}$, possibly over a different index set, such that $y_{\beta }\downarrow 0$ and for every $\beta$ there exists ${\alpha }_0$ such that $\{\{\pm (x_{\alpha }-x){\}}^u,y{\}}^l\subseteq \{y_{\beta }{\}}^l$, whenever $\alpha \ge {\alpha }_0$ and for all $0\le y\in X$. 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.

10 pages