Proof/disprove contunuity of a map
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
70645
Borel set preserved by continuous map
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
56567
Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
2251
Can someone give me a hint on how to prove this?
41617
If a $C^1$ map $f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is expanding ($\|f(x)-f(y)\|\geq\|x-y\|$), which of these must be true?
12104
How to prove this result involving the quotient maps and connectedness?
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
134120
Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
86107
Map bounded if composition is bounded
123891
There are finitely many maps on nonnegative integers satisfying $\phi(ab)=\phi(a)+\phi(b)$
15095
continuous onto map from $(0,1)\to (0,1]$
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
76234
Is this vector-valued map Hölder-continuous?
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.