$\{x^k\}^\infty_{k=0}$ is not basis in $C[0;1]$
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
79307
How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
158353
If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.
14840
$c_0$ is a closed subspace of $l^{\infty}$
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
74145
How to prove $x^{n}$ is not uniformly continuous
47231
The space $C^0([0;1],\mathbb{R})$ of all continuous, real-valued functions on $[0,1]$ is not reflexive.
52596
A basis for $k(X)$ regarded as a vector space over $k$
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
59929
Why is $(e_n)$ not a basis for $\ell_\infty$?
156457
Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$