Show that $j_{*}j^{-1}\mathcal{F}_{x}=\mathcal{F}_{x}$ if $x\in Z$ and $0$ otherwise, if $j:Z\rightarrow X$ is a closed subscheme of $X$
132407
inverse image presheaf property
33586
Prove the field of fractions of $F[[x]]$ is the ring $F((x))$ of formal Laurent series.
126989
Prove that $g(z)=\overline{f(z)}$ is complex diﬀerentiable at $a$ if and only if $f'(a) = 0$.
116768
Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
51898
Show that $\operatorname{Hom}_{R} (R,M) \cong M$
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
157420
Question about Subrings and integraly closed
106585
Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
92774
Prove that a linear subspace of $C([0,1])$ is closed
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
135422
$\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A') \Rightarrow A \cong A'$, proof verification
125962
The set $A'$ is closed in a $T_1$ space