Given analytic function $f$, why is $f: (w,z) \mapsto (f(z)-f(w))(z-w)^{-1}$ continuous?
58664
Proving a function is continuous for a fixed variable
146846
Why is this function continuous, unlike the Dirichlet function?
128658
Analyticity of $\overline {f(\bar z)}$ given $f(z)$ is analytic
55138
An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
12997
Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
56567
Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
136011
Must $f$ be continuous?
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
3349
For $f$ an analytic function, what is
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
145368
How to show $f:Y\to X^{+}$ is continuous?
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$