 They were introduced by and Myles Tierney.If "E" is a topos, then a topology on "E" is a morphism "j" from the subobject classifier Ω to Ω such that "j" preserves truth (formula_1), preserves intersections (formula_2), and is idempotent (formula_3).Given a subobject formula_4 of an object "A" with classifier formula_5, then the composition formula_6 defines another subobject formula_7 of "A" such that "s" is a subobject of formula_8, and formula_8 is said to be the "j"-closure of "s".