Totally unordered locale
= Totally unordered locale
{title2=$T_U$}
A <locale> is totally unordered when $f^*\leq g^*$ for two maps into it implies $f=g$, for every common domain. This tests generalized points rather than just ordinary points. Every <Hausdorff locale> has this property: comparable maps annihilate the complement of the diagonal and hence factor through the diagonal.