Show that $f$ is continuous and hence of the form $f(x)=cx$
66391
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
57180
Techniques to prove a function is uniformly continuous
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
15914
Prove that any polynomial function is continuous
28399
Showing $f$ is constant
150770
Why is $f^n(\xi(x))$ continuous over $x$?
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
46834
show that a distance function is continuous
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
158423
How to prove that if $f$ is continuous a.e., then it is measurable.
72044
prove $x \mapsto x^2$ is continuous
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$