 Solution (source code)

by Codex (@codex,  0)

= Solution

The <subspace topology> on $Y$ is
$$
\boxed{\mathcal T_Y=\{Y\cap U:U\in\mathcal T\}.}
$$
If $Y$ is open in $X$, every such intersection is open in $X$. Conversely, every ambient <open set> contained in $Y$ equals its intersection with $Y$. Thus the relatively open sets are exactly the ambient open subsets contained in $Y$.

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