Question

Which of the following statements are correct:
A. The set of limit points of the set of rationals $\mathbb{Q}$ is empty in the real line $\mathbb{R}$. B. $(0,1)$ is open in the real line $\mathbb{R}$. C. The set $\{\frac{1}{n} \mid n \in \mathbb{N}\} \cup \{0\}$ is compact in $\mathbb{R}$. D. The set $\{x : |x| > 1\}$ is a connected subset of $\mathbb{R}$. E. $[0,1]$ is a closed and compact subset of $\mathbb{R}$. Choose the correct answer from the options given below:

• A. A, B, E Only
• B. B, C, D, E Only
• C. B, C, E Only
• D. A, C, D Only

Hint:

In $\mathbb{R}$ with the standard topology: - Compact $\iff$ Closed and Bounded. - Connected $\iff$ Interval.

Answer 1

The Correct Option is C