No bounded linear surjectivity from $\ell^2(\mathbb{N})$ to $\ell^1(\mathbb{N})$
93923
No surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
20199
Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
55752
Prove that $n+1$ vectors in $\mathbb{R}^n$ cannot be linearly independent
80618
Surjective bounded operator in Banach spaces without bounded right-inverse
111689
Surjective, but not injective endomorphism
48990
Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ surjective
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
1148
Curious limit of a sequence used to prove Etemadi's SLLN
17262
Bounded operator that does not attain its norm
145668
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
79285
Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
118903
The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product
21391
Proving Functions are Surjective
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space