$\forall t \in \mathbb{R}, e^{i \alpha_n t} \rightarrow 1 \implies \alpha_n \rightarrow 0$?
97392
If $e^{itx_n}$ converges for every $t\in\mathbb R$, then does $x_n$ converge?
77735
When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
60485
Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
4834
Proving that unconditional convergence is equivalent to absolute convergence
88311
Linear functional f(v)=0 imply v=0
2105
$\langle Tu\;|\;u\rangle=0,\;\forall u\in E \Longrightarrow T=0$?
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $
1760
Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$?
108837
How to show that $\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$?
57581
Let $E$ be measurable and define $f:E\rightarrow\mathbb{R}$ such that $\{x\in E : f(x)>c\}$ is measurable for all $c\in\mathbb{Q}$, is $f$ measurable?
108329
If $T\alpha=c\alpha$, then there is a non-zero linear functional $f$ on $V$ such that $T^{t}f=cf$
82771
Proving that any polynomial $p:\mathbb{R}\rightarrow \mathbb{R}$ is not bounded, but its restriction to any bounded set is bounded
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
20789
If $\Sigma \vdash \varphi$ then $\Sigma \vdash \forall x \varphi$. Why when $(\varphi \implies \forall x \varphi)$ is not true?
152105
When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?