I only know that they are $T_2$ and second countable.
2026-03-29 08:35:28.1774773328
Are $\mathbb{RP}^n$ and $\mathbb{CP}^n$ metrizable?
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Since $\mathbb{RP}^n$ and $\mathbb{CP}^n$ are compact and $T_2$, they are regular ($T_1 + T_3$). Hence, by Urysohns metrization theorem, they are also metrizable.