9. Compactness I

Compact Subsets — Quiz

Test your understanding of compact subsets with 5 practice questions.

Practice Questions

Question 1

Which statement best describes a compact subset in a topological space?

Question 2

Which of the following is a compact subset of $\mathbb{R}$ with the usual topology?

Question 3

In $\mathbb{R}^n$, which property is guaranteed for every compact subset?

Question 4

Which theorem states that in $\mathbb{R}^n$, a subset is compact if and only if it is closed and bounded?

Question 5

Suppose $K$ is compact and $A$ is a closed subset of $K$. What can be concluded about $A$?