I am doing the exercises in the book Topology(2nd edition) by Munkres. Here is my question(page 127, question 4(a)):
Let $h:R\to R^\omega$ be a function defined by $h(t)=(t, t/2, t/3, \ldots)$ where $R^\omega$ is in the uniform topology. Is $h$ continuous?
I have been able to determine that $h$ is continuous in the product but not continuous in the box topology. However, I cannot then deduce what will happen in the uniform topology since
"product $\subset$ uniform $\subset$ box"
does not help in this direction.
Please, help. Thank you.