Is a function $f:\mathbb R\to\mathbb R$ such that $f(x+y)=f(x)+f(y)$ always continuous?
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
33304
Let $f$ be a continuous function satisfying $\lim \limits_{n \to \infty}f(x+n) = \infty$ for all $x$. Does $f$ satisfy $f(x) \to \infty$?
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
44574
Continuity of absolute value of a function
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
27800
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
76009
Can a continuous function from the reals to the reals assume each value an even number of times?
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
143174
property of continuous function
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
141842
Is the convolution of two continuous functions continuous?
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
110885
Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?