Jeremy Irons Dragons" (2000) and Rupert Gould in "Longitude" (2000). He played the Über-Morlock in the film "The Time Machine" (2002). In 2004, Irons played Severus Snape in Comic Relief's "Harry Potter" parody, "Harry Potter and the Secret Chamberpot of Azerbaijan". In 2005, he appeared in the films "Casanova" opposite Heath Ledger, and Ridley Scott's "Kingdom of Heaven". He has co-starred with John Malkovich in two films, "The Man in the Iron Mask" (1998) and "Eragon" (2006), though they did not have any scenes together in the latter. In 2008, Irons co-starred with Ed Harris and Viggo Mortensen in "Appaloosa", directed by
Directed set this setting, a subset "A" of a partially ordered set ("P",≤) is called a directed subset if it is a directed set according to the same partial order: in other words, it is not the empty set, and every pair of elements has an upper bound. Here the order relation on the elements of "A" is inherited from "P"; for this reason, reflexivity and transitivity need not be required explicitly. A directed subset of a poset is not required to be downward closed; a subset of a poset is directed if and only if its downward closure is an ideal.