Show that $C^1([a,b])$ is a complete space w.r.t. some special metric
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
140692
Existence of a complete metric on $(0,1)$
63516
$C^1[0,1]$ is not complete with respect to sup norm
92774
Prove that a linear subspace of $C([0,1])$ is closed
10907
Necessity of completeness of the inner product space in Riesz representation theorem
65809
Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
118272
Show that $L^1$ is strictly contained in $(L^\infty)^*$
92588
Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
108740
$C^1[a,b]$ is closed in $C[a,b]$
143674
Space of bounded functions is complete
6227
Showing diffeomorphism between $S^1 \subset \mathbb{R}^2$ and $\mathbb{RP}^1$
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
90628
The metric spaces are Tychonoff spaces
27652
metric on the Euclidean Group
60981
Understanding relation between Quotient Space and $S^1$