For every integer $n \geq 0$, the complex [projective space](/page/Projective%20Space) $\mathbb{C}\mathbb{P}^n$, equipped with its standard [quotient topology](/page/Quotient%20Topology) from $\mathbb{C}^{n+1} \setminus \{0\}$ under the [equivalence relation](/page/Equivalence%20Relation)
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\begin{align*}
z \sim w \iff w = \lambda z \text{ for some } \lambda \in \mathbb{C}^\times,
\end{align*}