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Trance-0
2025-12-05 11:53:00 -06:00
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@@ -112,7 +112,7 @@ Recall that $\mathbb{R}_{\ell}$ with lower limit topology is normal. But $\mathb
This shows that $\mathbb{R}_{\ell}$ is not metrizable. Otherwise $\mathbb{R}_{\ell}\times \mathbb{R}_{\ell}$ would be metrizable. Which could implies that $\mathbb{R}_{\ell}$ is normal.
#### Theorem of metrizability
#### Theorem of metrizability (Urysohn metirzation theorem)
If $X$ is normal and second countable, then $X$ is metrizable.