Residue

The residue of a flag, $F$, in an incidence geometry, $$\Gamma = (X,*,t,I)$$, is an incidence system $$\Gamma_F = (X_F, *_F, t_F, I_F)$$ where
 * $$X_F$$ is the set of elements of, not in $F$, that are incident on every element of $F$.
 * $$I_F$$ is the set of types of $$X_F$$, $$t(X_F)$$. It is equivalent to $$I\setminus t(F)$$.
 * $$*_F$$ is $$ restricted to the domain of $$X_F$$.
 * $$t_F$$ is $t$ restricted to the domain of $$X_F$$.

An incidence structure is residually connected if every residue of rank 2 or greater has a connected incidence graph.