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

在本文中，我们将研究\（{\\ t​​ilde {o}} \） -在（部分）有序向量空间中的收敛性，并研究在向量空间V中的一种收敛性。如果存在有序向量空间W和从V到W的算子T，则向量空间V称为半阶向量空间（简称半阶空间）。这样，我们说V是关于\（\ {W，T \} \）的半阶空间。净\（\ {x_ \ alpha \} \ subseteq V \）被称为\（{{{W，T \}} \\）-阶收敛到向量\（x \ in V \）（简而言之我们写\（X_ \阿尔法\ xrightarrow {\ {W，T \}} X \） ），每当存在一个净\（\ {Y_ \测试\} \）在W¯¯满足\（Y_ \测试\ DownArrow中文0 \）在W中，对于每个\（\ beta \），都存在\（\ alpha _0 \），使得\（\ pm（Tx_ \ alpha -Tx）\ le y_ \ beta \）每当\（\ alpha \ ge \ alpha _0 \）。在这份手稿中，我们研究和研究\（\ {W，T \} \）-收敛网络的某些性质以及它在部分有序向量空间中与其他阶收敛的关系。假设\（V_1 \）和\（V_2 \）是相对于\（\ {{W_1}，T_1 \} \）的半序空间和\（\ {W_2，T_2 \} \）。操作者小号从\（V_1 \）到\（V_2 \）被称为半阶连续，如果\（X_ \阿尔法\ xrightarrow {\ {{W_1}，T_1 \}} X \）意味着\（Sx_ \阿尔法\ xrightarrow {\ {W_2，T_2 \}}} Sx \）每当\（\ {x_ \ alpha \} \ subseteq V_1 \）。我们研究了这种新的运算符分类的属性。