(Theorem) The uniform topology is between the box and product topologies

Theorem (Munkres 20.4): The uniform topology is “between” the box and product topologies

On the generalized product ${\mathbb{R}}^J$ with arbitrary indexing set $J$, the box topology is finer than the uniform topology, and the uniform topology is finer than the product topology. Further, $J$ is infinite, then all three are distinct.