 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $p:X\to X/R$ send a point to its <equivalence class>. The <quotient topology> is
$$
\boxed{U\subseteq X/R\text{ is open exactly when }p^{-1}(U)\text{ is open in }X.}
$$
It is the finest <topology> on the quotient making $p$ continuous.

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