Let $\{a_n\}\in\mathbb R^{\mathbb N}$. Does there exist $h\in C^\infty(\mathbb R)$ with $h^{(n)}(0)=a_n$ for every $n$?
21407
Every power series is the Taylor series of some $C^{\infty}$ function
116273
Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
67084
Prove or disprove that $\lim_{n \to \infty} {n \choose k} / a^n = 0$ for all $k \in \mathbb{Z_+}, a \in \mathbb{R}: a> 1$.
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
119804
If $\lim_{n\to \infty}a_n = a\in \mathbb{R}$ . Prove that $\limsup_{n\to \infty}a_n x_n=a\limsup_{n\to \infty}x_n$ .
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
53425
Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
33397
Sobolev space $H^s(\mathbb{R}^n)$ is an algebra with $2s>n$
157203
Let $\{f_k\}_{k=1}^\infty\in L^{loc}_1(\mathbb R^n)$, show $\{f_k^2\}_{k=1}^\infty$ does not converge in $\mathscr{D}^\prime(\mathbb R^n)$
121198
$W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$?
105772
Definition of $\mathbb{R}^\infty$
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
22890
Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
47026
if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$