Minority Report (film) composed and conducted by John Williams and orchestrated by John Neufeld, with vocals by Deborah Dietrich. Williams normally enters Spielberg productions at an early stage, well before the movie starts shooting. For "Minority Report" however, his entry was delayed due to his work on "", and he joined the film when it was nearly completed, leaving him scant production time. The soundtrack takes inspiration from Bernard Herrmann's work. Williams decided not to focus on the science fiction elements, and made a score suitable for film noir. He included traditional noir elements such as a female singer in the Anne Lively
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