A region in $\mathbb { C }$ is a non-empty open connected set. Select all the statement(s) that are true. (A) Let $f$ be a function on a region $\Omega$ such that the integral of $f$ along the boundary of any closed triangle in $\Omega$ is zero. Then $f$ is analytic on $\Omega$. (B) There exist a region $\Omega$ containing the real interval $( 0,1 )$ and a non-zero analytic function $f : \Omega \rightarrow \mathbb { C }$ such that $f \left( \frac { 1 } { n } \right) = 0$ for all positive integers $n$. (C) Let $f$ be an analytic function on $\mathbb { C } \backslash \{ 0 \}$ with an essential singularity at $z = 0$. Then $\lim _ { z \rightarrow 0 } | f ( z ) | = \infty$. (D) Every bounded analytic function on $\mathbb { C } \backslash \{ 0 \}$ is constant.
A region in $\mathbb { C }$ is a non-empty open connected set. Select all the statement(s) that are true.\\
(A) Let $f$ be a function on a region $\Omega$ such that the integral of $f$ along the boundary of any closed triangle in $\Omega$ is zero. Then $f$ is analytic on $\Omega$.\\
(B) There exist a region $\Omega$ containing the real interval $( 0,1 )$ and a non-zero analytic function $f : \Omega \rightarrow \mathbb { C }$ such that $f \left( \frac { 1 } { n } \right) = 0$ for all positive integers $n$.\\
(C) Let $f$ be an analytic function on $\mathbb { C } \backslash \{ 0 \}$ with an essential singularity at $z = 0$. Then $\lim _ { z \rightarrow 0 } | f ( z ) | = \infty$.\\
(D) Every bounded analytic function on $\mathbb { C } \backslash \{ 0 \}$ is constant.