Does there exist a continuous function $f\colon \Bbb R\rightarrow \Bbb R$ such that $f(f(x))=-x$ for all $x\in\Bbb R$?
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
34344
Is a function that maps every compact set to a compact set continuous?
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$
96273
Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
2321
Can there be two distinct, continuous functions that are equal at all rationals?
102143
$f:\mathbb R\rightarrow \mathbb R$ be a continuous function such that $\int_{0}^{\infty}f(x)dx$ exists.
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
24017
Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
79285
Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
18126
If $f \colon [a,b] \rightarrow \mathbb{R}$, then show that there exists $c \in [a,b]$ such that $\int_a^c f = \int_c^b f$
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
27800
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
17223
Continuity of an inverse function.
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?