Let $X\subset \mathbb{R}^{2}$ be the subset
$$X=\left \{ \left ( x,y \right ) \left | x=0, \right |y \mid \leq 1\right \}\cup \left \{ \left ( x,y \right ) \mid 0 < x \leq 1, y=sin \frac{1}{x}\right \}.$$
Consider the following statements:
- $X$ is compact
- $X$ is connected
- $X$ is path connected
How many of the statements (i)-(iii) is /are true?
- $0$
- $1$
- $2$
- $3$
