Continuity and $f(x+y)=f(x)+f(y)$
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 $\mathbb R$
154572
Continuity of a function at an isolated point
110146
I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
71487
Real Analysis: Continuity of a Composition Function
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
142459
Continuity of a Function in Terms of Closure and Interior
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
145368
How to show $f:Y\to X^{+}$ is continuous?
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
143618
If a function $f$ is continuous $\implies$ $|f|$ is continuous.(Answered by Myself)
118207
Prove that the product of two continuous functions is continuous
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?