Solution
= Solution
{c}
Every map has $f(x)=f(x)$, so the relation is reflexive. Equality is symmetric, so $f(x)=f(y)$ for all the specified maps is equivalent to $f(y)=f(x)$; the relation is symmetric. If $x\mathcal Ry$ and $y\mathcal Rz$, every continuous map to every <Hausdorff space> has $f(x)=f(y)=f(z)$, proving $x\mathcal Rz$. Thus \b[$\mathcal R$ is an equivalence relation].