Show (0,1) is not compact
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
20135
Measure of  reals in $[0,1]$ which don't have $4$ in decimal expansion
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
149416
Show that $ \{\lnot,\leftrightarrow\} $ is not functional complete
99675
A closed ball in $l^{\infty}$ is not compact
154321
How to show that a limit diverges to $−∞$
142870
Prove the function is not differentiable at (0,0)
15095
continuous onto map from $(0,1)\to (0,1]$
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
78300
Showing a set is closed other than giving a counterexample?
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
6186
An Integrable function which is not essentially bounded on any subinterval of $[0,1]$
151958
How to show $f'(0)$ exist and is equal to $1$?
43283
More numbers between $[0,1]$ or $[1,\infty)$?
36514
Show that $45<x_{1000}<45.1$