query: Why is $\mathbb{R}^2$ endowed with the taxicab metric isomorphic to the infinity distance model of the cartesian real plane? (Hartshorne exercise 8.9)
positive_passages.docid: 20556
positive_passages.text: Isomorphism between two models of Hilbert's Axioms with different notions of congruence
negative_passages.docid: 57816
negative_passages.text: $(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$
negative_passages.docid: 90110
negative_passages.text: Hyperbolic metric geodesically complete
negative_passages.docid: 24828
negative_passages.text: surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
negative_passages.docid: 62479
negative_passages.text: A isometric map in metric space is surjective?
negative_passages.docid: 27652
negative_passages.text: metric on the Euclidean Group
negative_passages.docid: 2348
negative_passages.text: Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
negative_passages.docid: 17748
negative_passages.text: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
negative_passages.docid: 132311
negative_passages.text: T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
negative_passages.docid: 92340
negative_passages.text: How many metrics are there on a set up to topological equivalence?
negative_passages.docid: 96363
negative_passages.text: How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
negative_passages.docid: 96567
negative_passages.text: Immersion of $\mathbb{R}$ to $\mathbb{R}^2$
negative_passages.docid: 664
negative_passages.text: Minkowski's complex Euclidean space vs. the real pseudo-Euclidean version
negative_passages.docid: 72211
negative_passages.text: Isomorphism involving Eilenberg-Maclane space, Tors.
negative_passages.docid: 71037
negative_passages.text: Is exponential map locally a diffeomorphism w.r.t. base point?
negative_passages.docid: 120404
negative_passages.text: Showing that the geodesics in hyperbolic upper half-plane model are half circles
negative_passages.docid: 65809
negative_passages.text: Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric