Let ${\mathbf{Top}}_d$, ${\mathbf{Top}}_w$ and Sob be the category of all d-spaces, that of all well-filtered spaces and that of all sober spaces respectively. For a full subcategory K of ${\mathbf{Top}}_d$ containing Sob, it is proved that the product of an arbitrary family of K-determined sets is a K-determined set and if K is adequate, then the K-reflection preserves arbitrary products of $T_0$ spaces. In particular, the Keimel-Lawson reflection, well-filtered reflection and d-reflection all preserve arbitrary products of $T_0$ spaces, and DCPO-completion preserves the product of a family $\{P_i:i\in I\}$ of posets if the Scott topology of the product ${\prod }_{i\in I}{P}_i$ is the product of the Scott topologies of the factors.

让 ${\mathbf{最佳}}_d$， ${\mathbf{最佳}}_w$和点Sob是所有的类别d，所有公过滤空间和分别所有清醒空间-spaces。对于K的完整子类别${\mathbf{最佳}}_d$证明含有Sob的任意族的K-确定集的乘积是K-确定集，如果K足够，则K-反射将保留${Ť}_0$空格。特别是，Keimel-Lawson反射，经过良好滤波的反射和d反射都保留了以下任意乘积：${Ť}_0$空格，并且DCPO -completion保留了系列产品$\{P_{\mathrm{一世}}：\mathrm{一世}\in \mathrm{一世}\}$ 如果产品的斯科特拓扑结构正确 ${\prod }_{\mathrm{一世}\in \mathrm{一世}}{P}_{\mathrm{一世}}$ 是因素的Scott拓扑的乘积。