3. Closure, Interior, and Boundary

Dense Sets — Quiz

Test your understanding of dense sets with 5 practice questions.

Practice Questions

Question 1

What does it mean for a set $A$ to be dense in a topological space $X$?

Question 2

In the real numbers $\mathbb{R}$ with the usual topology, which set is dense in $\mathbb{R}$?

Question 3

If $A$ is dense in $X$, what is $\overline{A}$?

Question 4

Which statement is equivalent to saying that $A$ is dense in $X$?

Question 5

Which set is dense in $\mathbb{R}$ with the usual topology?