If $f$ is continuous on all of $\mathbb{C}$ and analytic on $\mathbb{C}$ minus $ [-1,1]$ then $f$ is entire
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If $f: \mathbb{C} \to \mathbb{C}$ is continuous and analytic off $[-1,1]$ then is entire.
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analytic function on $\mathbb{C}$ such that $f\Bigl(\frac{1}{2n}\Bigr)=f\Bigl(\frac{1}{2n+1}\Bigr)=\frac{1}{2n}$
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Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
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Prove that $f$ analytic, $f(x) \in \mathbb{R}$ for all $x \in \mathbb{R}$ implies $f(\overline{z})=\overline{f(z)}$
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Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
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If $f: \mathbb{C} \to \mathbb{C}$ is analytic and not linear, then $z, f(z), f(f(z)), \dots$ are linearly independent functions over $\mathbb{C}.$
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proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
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Let $f (z) $ be an entire function such that $|f (z)|≤K|z|$, $∀z∈\mathbb{C}$, for some $K>0$. If $f (1) =i$, then$f (i) $ is
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$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
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$f:\mathbb C\rightarrow \mathbb C$ be an arbitrary analytic function satisfying $f(0)=0$ and $f(1)=2.$
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Understanding the definition of the order of an entire function in Ahlfors's Complex Analysis
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Show that if $f(z)$ is a continuous function on a domain $D$ such that $f(z)^N$ is analytic for some integer $N$, then $f(z)$ is analytic on $D$.
121957
Is $p\mapsto \|f\|_p$ continuous?
73547
Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
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Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
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If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
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Continuity of $L^1$ functions with respect to translation