10. Compactness II

Continuous Images Of Compact Spaces — Quiz

Test your understanding of continuous images of compact spaces with 5 practice questions.

Practice Questions

Question 1

What is the key fact about the continuous image of a compact space?

Question 2

Let $f:[0,1]\to \mathbb{R}$ be continuous. Which statement must be true about $f([0,1])$?

Question 3

Which theorem is used to conclude that $f(K)$ is compact when $K$ is compact and $f$ is continuous?

Question 4

Suppose $K$ is compact and $f:K\to Y$ is continuous. Which open-cover idea is central to proving $f(K)$ is compact?

Question 5

Which statement is true in general?