TIFR-2015-Maths-B-9

Question

Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by

$A=\left\{ y \in \mathbb{R}:y = \lim_{n \rightarrow \infty} f(x_{n}), \text {for some sequence}   x_{n} \rightarrow +\infty\right\}$

Then the set A is necessarily.

• A. $A$ connected set
• B. $A$ compact set
• C. $A$ singleton set 
• D. None of the above