7. Quotient Topology

Quotient Maps — Quiz

Test your understanding of quotient maps with 5 practice questions.

Practice Questions

Question 1

What is a quotient map $q:X\to Y$?

Question 2

If $q:X\to Y$ is a quotient map and $U\subseteq Y$ satisfies $q^{-1}(U)$ is open in $X$, what can be concluded about $U$?

Question 3

Suppose $q:X\to Y$ is a quotient map. Which of the following is always true about a subset $V\subseteq Y$?

Question 4

Which of the following best describes the relation between a quotient map and the quotient topology on $Y$?

Question 5

Let $q:X\to Y$ be a quotient map and let $A\subseteq Y$. Which condition is equivalent to $A$ being open in $Y$?