is $[0,1]\backslash \mathbb{Q}$ totally bounded?

Question

I learnt totally bounded by myself. Now, I am still trying to understand the definition and looking for counterexamples which is totally bounded but not compact. The below is some of counterexamples:

1. $[0,1)$,

2. $(0,1)$,

3. $[0,1]\cap \mathbb{Q}$.

I am end up with the following question: is $[0,1]\backslash \mathbb{Q}$ totally bounded?

Answer 1

Every subset of finite-dimensional Euclidian space is totally bounded if and only if it is bounded. Which means that every subset of $\left[0;1\right]$ is totally bounded.