query: Why is this map homeomorphism?
positive_passages.docid: 18034
positive_passages.text: Is there an equivalence relation of which the quotient topology is homeomorphic to codomain of a quotient map?
negative_passages.docid: 37635
negative_passages.text: Diffeomorphism group of the unit circle
negative_passages.docid: 142652
negative_passages.text: When is the product of two quotient maps a quotient map?
negative_passages.docid: 25874
negative_passages.text: Showing that a certain map is not flat by explicit counterexample
negative_passages.docid: 149605
negative_passages.text: Homeomorphism from $[0,1]\times[0,1]$ to $\overline{D}(0,1)$?
negative_passages.docid: 100736
negative_passages.text: Why every map $f : S^n \to T^n (n>1)$ has topological degree zero?
negative_passages.docid: 44069
negative_passages.text: Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
negative_passages.docid: 52629
negative_passages.text: Example 1, Sec. 22 in Munkres' TOPOLOGY, 2nd edition: How to verify that this map is closed?
negative_passages.docid: 88981
negative_passages.text: Explicit Homeomorphism from $\mathbb{R}^2$ to open disk
negative_passages.docid: 6118
negative_passages.text: Homeomorphism of the real line-Topology
negative_passages.docid: 12060
negative_passages.text: Homeomorphism to graph
negative_passages.docid: 37092
negative_passages.text: Homeomorphism between a cone in a compact space and this compactification
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)
negative_passages.docid: 27757
negative_passages.text: $\mathbb{R}\to\mathbb{R}$ Diffeomorphism with special property
negative_passages.docid: 129623
negative_passages.text: A shrinking map that is not a contraction no fixed point.
negative_passages.docid: 61593
negative_passages.text: Adjoint map is Lie homomorphism
negative_passages.docid: 147350
negative_passages.text: Homeomorphism between $\prod X_i$ and the Cantor set