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 notions of limit used in analysis. Directed sets also give rise to direct limits in abstract algebra and (more generally) category theory. In addition to the definition above, there is an equivalent definition. A directed set is a set "A" with a preorder such that every finite subset of "A" has an upper bound. In this definition, the existence of an upper bound of the empty subset implies that "A" is nonempty. Examples of directed sets include: Directed sets are a more general concept than (join) semilattices: every join semilattice is a directed set, as the join or least upper