4. Continuity and Homeomorphisms

Equivalent Characterizations — Quiz

Test your understanding of equivalent characterizations with 5 practice questions.

Practice Questions

Question 1

In a topological space, which condition is equivalent to saying that a function $f:X\to Y$ is continuous?

Question 2

Suppose $f:X\to Y$ is continuous. Which statement about closed sets must be true?

Question 3

Which condition is another equivalent way to state that $f:X\to Y$ is continuous?

Question 4

Let $f:X\to Y$ be a function between topological spaces. Which condition alone is enough to guarantee that $f$ is continuous?

Question 5

A homeomorphism is a function $f:X\to Y$ with what property?