4. Continuity and Homeomorphisms

Continuity Via Inverse Images — Quiz

Test your understanding of continuity via inverse images with 5 practice questions.

Practice Questions

Question 1

In the inverse-image definition of continuity, what must be true for every open set $U$ in the codomain under a continuous function $f$?

Question 2

Which statement correctly describes the inverse image of a set $A$ under a function $f$?

Question 3

Suppose $f:X \to Y$ is continuous and $U \subseteq Y$ is open. What can be concluded about $f^{-1}(U)$?

Question 4

Which statement is a standard equivalent characterization of continuity in topology?

Question 5

Let $f:X \to Y$ be continuous. If $V \subseteq Y$ is closed, what must be true about $f^{-1}(V)$?