Show that $\mathcal{O}_{\mathbb{P^1}}(-1)$ has no nonzero global sections.
8654
Global sections of $\mathcal{O}(-1)$ and $\mathcal{O}(1)$, understanding structure sheaves and twisting.
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
132382
Showing a set is nowhere dense in $C([0,1])$
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
116378
Nonhomeomorphic subsets of the plane
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
102079
If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
71071
Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
84386
Domain strictly contained in the intersection of localizations at the primes of height one
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
40996
Proving that free modules are flat (without appealing projective modules)
154322
Localizing the zeros of $z^4+z+1$