7. Continuity

Continuity On Compact Sets — Quiz

Test your understanding of continuity on compact sets with 5 practice questions.

Practice Questions

Question 1

Which statement is guaranteed by the Extreme Value Theorem for a function $f$ continuous on a compact set $K$?

Question 2

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

Question 3

If $f$ is continuous on a compact set $K$, what must be true?

Question 4

What theorem states that a continuous function on a compact set is uniformly continuous?

Question 5

If $f:K\to\mathbb{R}$ is continuous and $K$ is compact, what can be said about $f(K)$?