We introduce a preclosure on sets of reflections called the Bruhat preclosure which is defined by a twisting of the Bruhat graph of a Coxeter group. By a conjecture of Dyer; this preclosure is another method of finding the join in the weak order of Coxeter groups using the inversion set. This conjecture has been solved for dihedral groups and for the symmetric group, but is still open for all other finite Coxeter groups. We go over this conjecture and its implications in infinite Coxeter groups.