Showing the unit ball in $l^{\infty}$ is not compact.
31002
Proving that the unit ball in $\ell^2(\mathbb{N})$ is non-compact
103383
Let $\{K_i\}_{i=1}^{\infty}$ a decreasing sequence of compact and non-empty sets on $\mathbb{R}^n.$ Then $\cap_{i = 1}^{\infty} K_i \neq \emptyset.$
143254
Closed ball not a manifold.
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
120623
Unit sphere in $\mathbb{R}^\infty$ is contractible?
117419
Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
145668
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
2129
Showing that the derivative operator is not bounded on $L^2 (\mathbb{R})$
110526
Why is $l^\infty$ not separable?
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
37812
Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.
112501
A funtion and its fourier transformation cannot both be compactly supported unless f=0
156727
A step in the proof of Characterization of $W^{1,\infty}$
151796
There is not an holomorphic function on a bounded domain such that $\lim_{z \to w} f(z)= \infty$ for every $w \in Fr(\Omega)$
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact