Let $f : \mathbb{R}^{2} \to \mathbb{R}$ be of class $C^{1}$. Show that $f$ not is injective.
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
20955
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
107076
Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$