continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
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?
28730
product of two uniformly continuous functions is uniformly continuous
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
138105
Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
100839
If two continuous functions are equal almost everywhere on $[a,b]$, then they are equal everywhere on $[a,b]$
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
110885
Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
62817
Functions which are Continuous, but not Bicontinuous
147299
Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
32359
Inner product of two continuous maps is continuous
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$