Semi-order Continuous Operators on Vector Spaces

In this manuscript, we will study \({\tilde{o}}\)-convergence in (partially) ordered vector spaces and a kind of convergence space V. A V is called semi-order (in short space), if there exist an W operator T from into W. way, say that with respect to \(\{W, T\}\). net \(\{x_\alpha \}\subseteq V\) said be \({\{W,T\}}\)-order convergent \(x\in write \(x_\alpha \xrightarrow {\{W, T\}}x\)), whenever exists \(\{y_\beta \}\) satisfying \(y_\beta \downarrow 0\) for each \(\beta \), \(\alpha _0\) such \(\pm (Tx_\alpha -Tx) \le y_\beta \) \ge \alpha _0\). investigate some properties \(\{W,T\}\)-convergent nets its relationships other order partially spaces. Assume \(V_1\) \(V_2\) are \(\{{W_1}, T_1\}\) \(\{W_2, T_2\}\), respectively. An S continuous, {\{{W_1}, T_1\}}x\) implies \(Sx_\alpha {\{W_2, T_2\}}Sx\) V_1\). We new classification operators.