If $f(x+y)=f(x)+f(y)$ in real numbers, does the function $f$ have to be continuous?
33315
Many other solutions of the Cauchy's Functional Equation
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
76009
Can a continuous function from the reals to the reals assume each value an even number of times?
141842
Is the convolution of two continuous functions continuous?
100786
Does a continuous function take Cauchy sequences to Cauchy sequences?
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
86472
$f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
142873
What does the function f: x ↦ y mean?
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
33499
For which $a\in \mathbb{R}$ is $f(x,y) = \frac{xy^a}{x^2+y^2}$ with $f(0,0)=0$ continuous?
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
44574
Continuity of absolute value of a function
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
71487
Real Analysis: Continuity of a Composition Function