Solution
= Solution
The <quotient set> $X/\mathcal R$ consists of the <equivalence classes>. Let $p(x)=[x]$. Equip that set with the <quotient topology>
$$
\boxed{U\subseteq X/\mathcal R\text{ open}\iff p^{-1}(U)\text{ open in }X.}
$$
Preimages preserve the empty set, whole set, arbitrary unions and finite intersections, so this is a <topology>. The canonical projection is <continuous> and <surjective>, and the displayed equivalence specifies the <quotient space> completely.