If $dF_p$ is nonsingular, then $F(p)\in$ Int$N$
68514
Let $M$ be a smooth manifold and let $N$ be a manifold with boundary. If $dF_{p}$ is an isomorphism, then $F\left(p\right)\in\mbox{int}M $.
148355
Regarding Goldstein's claim that $\mathbf{F} = \dot{\mathbf{p}}$
158011
$C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
13732
$||f||_p\to ||f||_\infty$ under general assumptions
25795
Density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
157426
Proving that:$\int_X f_n g \, d\mu \to \int_X fg \, d\mu$ for all $g$ in $\mathscr{L}^q (X)$
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
84301
Showing that some Function on the Unit Disc is injective
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
141418
When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
104263
How to show that $f'(x)<2f(x)$
94365
How to prove that if $D$ is countable, then $f(D)$ is either finite or countable?
87570
Prove that if a function's average is nondecreasing then the function is nondecreasing.
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
26126
$f \in L^1$, but $f \not\in L^p$ for all $p > 1$
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$