Question 1
In subspace topology, what does it mean for a map $f:A\to Y$ to be continuous when $A$ is a subspace of a topological space $X$?
Question 2
Let $A\subseteq X$ and let $U\subseteq X$ be open. Which set is guaranteed to be open in the subspace topology on $A$?
Question 3
Suppose $A\subseteq X$ and $f:X\to Y$ is continuous. What can be said about the restriction $f|_A:A\to Y$?
Question 4
Let $A\subseteq X$ have the subspace topology. Which statement correctly describes continuity of a function $g:A\to Y$?
Question 5
Which of the following is a common way to prove that a function $g:A\to Y$ is continuous, where $A$ has the subspace topology from $X$?
