6. Topology of the Real Line

Heine-borel Theorem — Quiz

Test your understanding of heine-borel theorem with 5 practice questions.

Practice Questions

Question 1

Which statement is the Heine-Borel theorem for subsets of $\mathbb{R}$?

Question 2

Which set is compact in $\mathbb{R}$?

Question 3

Which property does $(0,1)$ fail, so it is not compact in $\mathbb{R}$?

Question 4

According to the Heine-Borel theorem, every open cover of a compact set in $\mathbb{R}$ has what?

Question 5

Which set is not compact in $\mathbb{R}$?