query: How to prove formally that these two definitions of Complex projective space are same?
positive_passages.docid: 27629
positive_passages.text: How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification
negative_passages.docid: 21466
negative_passages.text: $P$ is projective . Show that $P$ is a direct summand of a free $R-$ module
negative_passages.docid: 124713
negative_passages.text: Projective space is not affine
negative_passages.docid: 148633
negative_passages.text: Description of varieties in $\mathbb{P}^2\times \mathbb{P}^1$
negative_passages.docid: 86741
negative_passages.text: Relation between different definitions of degree in complex geometry
negative_passages.docid: 141802
negative_passages.text: Prove that free modules are projective
negative_passages.docid: 118288
negative_passages.text: Complex structure on $\mathbb S^1 \times \mathbb S^3$
negative_passages.docid: 79367
negative_passages.text: Understanding the difference between two theorems related to $|G\,:\,K|=|H\,:\,K|\cdot|G\,:\,H|$.
negative_passages.docid: 104258
negative_passages.text: Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
negative_passages.docid: 115014
negative_passages.text: Classification of automorphisms of projective space
negative_passages.docid: 65333
negative_passages.text: Weighted projective space and projective space are isomorphic
negative_passages.docid: 106081
negative_passages.text: The Projection to a Projective Line is Holomorphic
negative_passages.docid: 40041
negative_passages.text: Proof of Non-Ordering of Complex Field
negative_passages.docid: 142698
negative_passages.text: Proving that the fundamental groups of two spaces with same homotopy type are isomorphic
negative_passages.docid: 18839
negative_passages.text: Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$
negative_passages.docid: 66548
negative_passages.text: proving topological equivalence
negative_passages.docid: 10350
negative_passages.text: Automorphisms of the complex plane