Results in this paper concern finding a cardinal number κ, as small as possible, such that every uniformly or proximally continuous mapping from a given subspace X of a product ${\prod }_I{X}_i$ into some A factorizes via a subspace of ${\prod }_J{X}_i$ with $|J|\le \kappa$. In some cases we substantially improve Vidossich theorem from [12]. Influenced by investigating locally co-presentable categories in [8], also cardinals κ are found such that the above factorization hold for all products ${\prod }_I{X}_i$ from an epireflective subclass $\mathcal{C}$ of Unif₂, their closed subspaces X and spaces A generating $\mathcal{C}$. That situation is close to factorizing maps on limits of inverse systems via limits of smaller inverse subsystems. We define and investigate a new cardinal function on uniform spaces helping to find a convenient factorization.

本文中的结果涉及找到一个尽可能小的基数κ，以便从产品的给定子空间X中的每个均匀或近端连续映射${\prod }_{\mathrm{一世}}{X}_{\mathrm{一世}}$通过一个子空间分解成一些A${\prod }_J{X}_{\mathrm{一世}}$ 和 $|J|\le \kappa$. 在某些情况下，我们大大改进了 [12] 中的 Vidossich 定理。受 [8] 中调查局部可表示类别的影响，还发现了基数κ，使得上述因式分解适用于所有产品${\prod }_{\mathrm{一世}}{X}_{\mathrm{一世}}$ 来自表面反射子类 $\mathcal{C}$的Unif ₂，它们的闭合子空间X和空间A生成$\mathcal{C}$. 这种情况接近于通过较小逆子系统的极限分解逆系统极限的映射。我们在统一空间上定义并研究了一个新的基数函数，以帮助找到方便的因式分解。