Let $f:\mathbb{R} \to \mathbb{R}$ be continuous satisfying: $f(x+y) = f(x) + f(y)$. Show $f$ is linear
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
152379
If $V_1, V_2$ are $\mathbb{Q}$-vector spaces and $f \colon V_1 \to V_2$ is additive, then $f$ is $\mathbb{Q}$-linear
145368
How to show $f:Y\to X^{+}$ is continuous?
127538
Show $f(x)=x\ln x$ is not uniformly continuous
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
95340
Locally bounded additive function is linear
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
114458
$f$ is entire and maps a rectangle to a rectangle, then $f$ is linear
849
$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?
154521
Linear functional $f$ is continuous at $x_0=0$ if and only if $f$ is continuous $\forall x\in X$?
94737
How to show $f$ is continuous at $x$ IFF for any sequence ${x_n}$ in $X$ converging to $x$ the sequence $f(x_n)$ converges in $Y$ to $f(x)$
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.