cmi-entrance 2015 Q4

cmi-entrance · India · pgmath 4 marks Not Maths
Choose the correct statement(s):
(A) There is a continuous surjective function from $[0,1)$ to $\mathbb{R}$;
(B) $\mathbb{R}$ and $[0,1)$ are homeomorphic to each other;
(C) There is a bijective function from $[0,1)$ to $\mathbb{R}$;
(D) Bounded subspaces of $\mathbb{R}$ cannot be homeomorphic to $\mathbb{R}$.
Choose the correct statement(s):\\
(A) There is a continuous surjective function from $[0,1)$ to $\mathbb{R}$;\\
(B) $\mathbb{R}$ and $[0,1)$ are homeomorphic to each other;\\
(C) There is a bijective function from $[0,1)$ to $\mathbb{R}$;\\
(D) Bounded subspaces of $\mathbb{R}$ cannot be homeomorphic to $\mathbb{R}$.