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 article) assume that a directed set is directed upward, unless otherwise stated. Beware that other authors call a set directed if and only if it is directed both upward and downward. Directed sets are a generalization of nonempty totally ordered sets. That is, all totally ordered sets are directed sets (contrast "partially" ordered sets, which need not be directed). Join semilattices (which are partially ordered sets) are directed sets as well, but not conversely. Likewise, lattices are directed sets both upward and downward. In topology, directed sets are used to define nets, which generalize sequences and unite the various