Prove X is banach iff $S(0,1)$ is complete.
34173
Banach spaces and their unit sphere
125776
If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
84264
the space of lipschitz function is complete with respect to some norm
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
151046
Closure of the invertible operators on a Banach space
92588
Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
21391
Proving Functions are Surjective
156161
Banach-Tarski theorem without axiom of choice
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
67625
$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$
87655
Consequence of the Hahn-Banach Theorem
136439
Where can I read the full proof of the Banach-Mazur theorem?
13848
Showing that if a subset of a complete metric space is closed, it is also complete
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$