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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.

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    You're inconsistent with $f$ and $h$.2011-10-04
  • 1
    http://at.yorku.ca/cgi-bin/bbqa?forum=homework_help_2003;task=show_msg;msg=0806.0001.00012011-10-04

3 Answers 3