query: Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
positive_passages.docid: 142174
positive_passages.text: Nonexistence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$
negative_passages.docid: 101319
negative_passages.text: Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
negative_passages.docid: 46863
negative_passages.text: Show that $g$ is injective
negative_passages.docid: 112131
negative_passages.text: Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
negative_passages.docid: 90010
negative_passages.text: Can we ascertain that there exists an epimorphism $G\rightarrow H$?
negative_passages.docid: 28798
negative_passages.text: Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
negative_passages.docid: 24828
negative_passages.text: surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
negative_passages.docid: 29582
negative_passages.text: Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
negative_passages.docid: 87027
negative_passages.text: There is no continuous injective function $f:\mathbb{R}^n\longrightarrow\mathbb{R}^m$
negative_passages.docid: 45710
negative_passages.text: Finishing a proof: $f$ is injective if and only if it has a left inverse
negative_passages.docid: 45432
negative_passages.text: Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
negative_passages.docid: 113799
negative_passages.text: Is there an injective $C^1$ curve dense in the plane?
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 156679
negative_passages.text: $K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
negative_passages.docid: 119702
negative_passages.text: Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
negative_passages.docid: 63836
negative_passages.text: Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
negative_passages.docid: 97391
negative_passages.text: Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space