Lawvere-Tierney topology
= Lawvere-Tierney topology
{c}
A Lawvere-Tierney topology on a topos is a morphism $j:\Omega\to\Omega$ satisfying, internally,
$$
j(\top)=\top,
\qquad j(jp)=j(p),
\qquad j(p\wedge q)=j(p)\wedge j(q).
$$
It is also called a local operator.
= Local operator
{synonym}