Solution
= Solution
If $A\subseteq X$, the <subspace topology> on $A$ is
$$
\{A\cap U:U\text{ is open in }X\}.
$$
If $\sim$ is an <equivalence relation> on $X$ and $q:X\to X/{\sim}$ is the natural projection, the <quotient topology> declares $V\subseteq X/{\sim}$ open exactly when $q^{-1}(V)$ is open in $X$. For topological spaces $X$ and $Y$, the <product topology> on $X\times Y$ has as a basis all sets $U\times V$ with $U$ open in $X$ and $V$ open in $Y$.