Let $A = \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 < 1\}$ and $B = \{(x,y) \in \mathbb{R}^2 \mid 1 < x^2 + y^2 < 2\}$, both taken with the subspace topology of $\mathbb{R}^2$. Choose the correct statement(s) from below: (A) Every continuous function from $A$ to $\mathbb{R}$ has bounded image; (B) There exists a non-constant continuous function from $B$ to $\mathbb{N}$ (in the subspace topology of $\mathbb{R}$); (C) For every surjective continuous function from $A \cup B$ to a topological space $X$, $X$ has at most two connected components; (D) $B$ is homeomorphic to the unit circle.
Let $A = \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 < 1\}$ and $B = \{(x,y) \in \mathbb{R}^2 \mid 1 < x^2 + y^2 < 2\}$, both taken with the subspace topology of $\mathbb{R}^2$. Choose the correct statement(s) from below:\\
(A) Every continuous function from $A$ to $\mathbb{R}$ has bounded image;\\
(B) There exists a non-constant continuous function from $B$ to $\mathbb{N}$ (in the subspace topology of $\mathbb{R}$);\\
(C) For every surjective continuous function from $A \cup B$ to a topological space $X$, $X$ has at most two connected components;\\
(D) $B$ is homeomorphic to the unit circle.