Rolle's theorem without compact domain hypothesis
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
88099
Not $\sigma$-compact set without axiom of choice
56446
A kind of converse of Lagrange's Theorem
52301
Omitting the hypotheses of finiteness of the measure in Egorov theorem
123132
Counterexample for a non-measurable function?
131000
A proof of a criterion of vanishing of a function.
111122
Proof of a theorem in Hilbert's system
119831
bounded operator $T$ is not compact then there exists an orthonormal sequence $e_n$ and $d>0$ such that $\|T(e_n)\|>d$ for all $n\in\Bbb{N}$?
84492
Can $X$ have compact connected components?
38354
A result similar to Schwarz lemma
26215
Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.
157213
Application of Luca's theorem
54957
The necessary and sufficient condition for a unit element in Euclidean Domain
76347
Shorter proof for some equvalences
47791
Root of continuous function using Rolle's Theorem
27899
Can we prove the existence of $A\cup B$ without the union axiom?
71479
Is there some elementary proof of invariance of domain?