query: Homeomorphism between $[0,\infty)^n$ with Upper Half-Space $\mathbb{H}^n$
positive_passages.docid: 144072
positive_passages.text: Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?
negative_passages.docid: 27757
negative_passages.text: $\mathbb{R}\to\mathbb{R}$ Diffeomorphism with special property
negative_passages.docid: 144246
negative_passages.text: Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
negative_passages.docid: 128301
negative_passages.text: Homeomorphism from square to unit circle
negative_passages.docid: 34699
negative_passages.text: A continuous bijection from a compact space to a $T_2$ space is always a homeomorphism
negative_passages.docid: 44559
negative_passages.text: Finding a homeomorphism $\mathbb{R} \times S^1 \to \mathbb{R}^2 \setminus \{(0,0)\}$
negative_passages.docid: 27746
negative_passages.text: Autohomeomorphism of the unit disk which is constant on the boundary, and which takes 0 to a prescribed point
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 152478
negative_passages.text: Is there a homeomorphism between the $n$-dimensional cube to the $n$-dimensional simplex that doesn't create hard corners?
negative_passages.docid: 145077
negative_passages.text: A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
negative_passages.docid: 65034
negative_passages.text: Are continuous self-bijections of connected spaces homeomorphisms?
negative_passages.docid: 46001
negative_passages.text: Can a finite group act freely (as homeomorphisms) on $\mathbb R^n$
negative_passages.docid: 83446
negative_passages.text: bijective continuous function on $\mathbb R^n$ not homeomorphism?
negative_passages.docid: 80212
negative_passages.text: Suppose that $X$ is a topological space and $x_0\in X$. Prove that $\widetilde{H_n}(X)=H_n(X,x_0)$ for all $n\geq 0$.
negative_passages.docid: 30178
negative_passages.text: Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
negative_passages.docid: 109498
negative_passages.text: Linear maps $f: M_n \longrightarrow \mathbb{R}$ such that $f(AB) = f(BA)$