query: A question about space quotient and homeomorphism
positive_passages.docid: 143140
positive_passages.text: When are quotients of homeomorphic spaces homeomorphic?
negative_passages.docid: 46970
negative_passages.text: If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
negative_passages.docid: 49503
negative_passages.text: Why does the natural quotient metric works in this case?
negative_passages.docid: 12060
negative_passages.text: Homeomorphism to graph
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 34293
negative_passages.text: Homeomorphism between pairs of letters
negative_passages.docid: 149605
negative_passages.text: Homeomorphism from $[0,1]\times[0,1]$ to $\overline{D}(0,1)$?
negative_passages.docid: 144072
negative_passages.text: Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?
negative_passages.docid: 91337
negative_passages.text: Is every self-homeomorphism homotopic to a diffeomorphism?
negative_passages.docid: 158127
negative_passages.text: Quotient space of $\Bbb C^n$ obtained by action of $S_n$
negative_passages.docid: 147350
negative_passages.text: Homeomorphism between $\prod X_i$ and the Cantor set
negative_passages.docid: 31479
negative_passages.text: homeomorphism of cantor set extends to the plane?
negative_passages.docid: 18034
negative_passages.text: Is there an equivalence relation of which the quotient topology is homeomorphic to codomain of a quotient map?
negative_passages.docid: 37092
negative_passages.text: Homeomorphism between a cone in a compact space and this compactification
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 154324
negative_passages.text: preservation of completeness under homeomorphism
negative_passages.docid: 157987
negative_passages.text: Can a space $X$ be homeomorphic to its twofold product with itself, $X \times X$?