query: Is the preimage of a dimension $m$ subspace of the projective space under the quotient map $q$ of dimension $m+1$
positive_passages.docid: 26780
positive_passages.text: Dimension of cone of projective variety
negative_passages.docid: 124713
negative_passages.text: Projective space is not affine
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 142652
negative_passages.text: When is the product of two quotient maps a quotient map?
negative_passages.docid: 70082
negative_passages.text: Show: Quotient space is homeomorphic to unit sphere
negative_passages.docid: 82814
negative_passages.text: Homework question on whether two quotient spaces are homeomorphic
negative_passages.docid: 121100
negative_passages.text: Rootspaces are $\mathop{ad}$ nilpotent
negative_passages.docid: 73773
negative_passages.text: $C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
negative_passages.docid: 101860
negative_passages.text: Relating the normal bundle and trivial bundles of $S^n$ to the tautological and trivial line bundles of $\mathbb{R}P^n$
negative_passages.docid: 113377
negative_passages.text: Empty preimage of an intersection implies empty intersection of the preimages
negative_passages.docid: 147752
negative_passages.text: Is the quotient map a homotopy equivalence?
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
negative_passages.docid: 101671
negative_passages.text: Describe the image of the set $\{z=x+iy:x>0,y>0\}$ under the mapping $w=\frac{z-i}{z+i}$
negative_passages.docid: 57653
negative_passages.text: Relation between line bundles over $\mathbb{P}^1$ in geometry and topology
negative_passages.docid: 143869
negative_passages.text: Showing that the norm of the canonical projection $X\to X/M$ is $1$
negative_passages.docid: 137093
negative_passages.text: What is the codimension of matrices of rank $r$ as a manifold?
negative_passages.docid: 124786
negative_passages.text: Prove that V contains a subspace of each dimension