An operator T from vector lattice E into topological vector space \((F,\tau )\) is said to be order-to-topology continuous whenever \(x_\alpha \xrightarrow {o}0\) implies \(Tx_\alpha \xrightarrow {\tau }0\) for each \((x_\alpha )_\alpha \subset E\). The collection of all order-to-topology continuous operators will be denoted by \(L_{o\tau }(E,F)\). In this paper, we will study some properties of this new class of operators. We will investigate the relationships between order-to-topology continuous operators and others classes of operators such as order continuous, order weakly compact and b-weakly compact operators. Under some sufficient and necessary conditions we show that the adjoint of order-to-norm continuous operators is also order-to-norm continuous and vice verse.

每当向量（x_ \ alpha \ xrightarrow {o} 0 \）暗示\（Tx_ \ ）时，从向量格E到拓扑向量空间\（（F，\ tau）\）的算子T就是从阶到拓扑连续的。每个\（（x_ \ alpha）_ \ alpha \ subset E \）的alpha \ xrightarrow {\ tau} 0 \）。所有从拓扑到拓扑的连续运算符的集合将由\（L_ {o \ tau}（E，F）\）表示。在本文中，我们将研究这种新型算子的一些性质。我们将调查，如订单不断，秩序弱紧凑和运营商的订单到拓扑连续运营商和其他类之间的关系b-弱紧凑型运算符。在某些充分必要的条件下，我们证明了从范数到范数的连续算子的伴随性也是从范数到范数的连续算子，反之亦然。