query: quotient by contractible space and homotopy equivalent?
positive_passages.docid: 147752
positive_passages.text: Is the quotient map a homotopy equivalence?
negative_passages.docid: 8799
negative_passages.text: Mapping homotopic to the identity map has a fixed point
negative_passages.docid: 93263
negative_passages.text: Can contractible subspace be ignored/collapsed when computing $\pi_n$ or $H_n$?
negative_passages.docid: 29359
negative_passages.text: Localisation isomorphic to a quotient of polynomial ring
negative_passages.docid: 10215
negative_passages.text: Differentiable manifolds as locally ringed spaces
negative_passages.docid: 95887
negative_passages.text: How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
negative_passages.docid: 128941
negative_passages.text: How to compute the topological space of fibered product of schemes?
negative_passages.docid: 69528
negative_passages.text: Metrizability of quotient spaces of metric spaces
negative_passages.docid: 144072
negative_passages.text: Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?
negative_passages.docid: 135126
negative_passages.text: Proving that the quotient manifold is orientable if and only if the group action is orientation-preserving
negative_passages.docid: 42552
negative_passages.text: Localisation is isomorphic to a quotient of polynomial ring
negative_passages.docid: 39652
negative_passages.text: Quotient of free module
negative_passages.docid: 115851
negative_passages.text: Why is this quotient space not Hausdorff?
negative_passages.docid: 81873
negative_passages.text: Is $(X,\mathcal T)$ necessarily an indiscrete space?
negative_passages.docid: 126881
negative_passages.text: (weak) homotopy equivalence
negative_passages.docid: 94059
negative_passages.text: Extending a Homotopy from $X \times [0,1]$ to $X \times \mathbb{R}$
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?