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Proper Filter
In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear in order and lattice theory, but also topology, whence they originate. The notion dual to a filter is an order ideal. Special cases of filters include ultrafilters, which are filters that cannot be enlarged, and describe nonconstructive techniques in mathematical logic. Filters on sets were introduced by Henri Cartan in 1937. Nicolas Bourbaki, in their book ''Topologie Générale'', popularized filters as an alternative to E. H. Moore and Herman L. Smith's 1922 notion of a net; order filters generalize this notion from the specific case of a power set under inclusion to arbitrary partially ordered sets. Nevertheless, the theory of power-set filters retains interest in its own right, in part for substantial applications in topology. Motivation Fix a partially ordered set (poset) . Intuitively, a filter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Filter Vs Ultrafilter
Filtration is a physical process that separates solid matter and fluid from a mixture. Filter, filtering, filters or filtration may also refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component that performs some operation on a multimedia stream * Information filtering system ** Email filtering, the processing of email to organize it according to specified criteria * Content-control software also known as an Internet filter * Wordfilter, a script typically used on Internet forums or chat rooms * Berkeley Packet Filter, filter expression used in the qualification of network data * DSL filter, a low-pass filter installed between analog devices and a telephone line * Helicon Filter, a raster graphics editor * Filter (large eddy simulation), a mathematical operation intended to remove a range of small scales from the solution to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
