$X$ is $T_0$ iff $\forall x,y \in X$ $x\ne y$ it holds that $\overline{\{x\}}\ne \overline{\{y\}}$.
2056
A space is $T_{0}$ if and only if the closures of singletons are distinct
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
150331
Whenever $f=T(x)$ then $f(x) \geq 0$. Prove $T$ is bounded by closed graph theorem.
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
147892
Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
128108
$Y=\prod_{n\in\mathbb{N}}X$.
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
51934
Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
837
Suppose that $(s_n)$ converges to $s$, $(t_n)$ converges to $t$, and $s_n \leq t_n \: \forall \: n$. Prove that $s \leq t$.
85818
$E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
122190
Kernel of $T$ is closed iff $T$ is continuous