Exercise 32.5

Question

Is $\mathbb{R}^\omega$ normal in the product topology? In the uniform topology?

Amit Awasthi · Accepted Answer

\begin{proof}
  Since $\mathbb{R}^\omega$ is metrizable in the product topology by Theorem $20.5$ and in the uniform topology by definition on p.~124, both are normal by Theorem $32.2$.
\end{proof}

Exercise 32.5

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Exercise 32.5

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