A filtrator is a pair consisting of a poset (the base of the filtrator) and its subset (the core of the filtrator). The set is considered as a poset with the induced order.
Having fixed a filtrator and an , we define:
Probably the most important example of a filtrator is a primary filtrator that is the pair where is the set of filters on a poset ordered reverse to set-theoretic inclusion of filters and is the set of principal filters on this poset. For a filter we have essentially equivalent with the set .
- 1 Victor Porton. http://www.mathematics21.org/binaries/filters.pdfFilters on posets and generalizations. International Journal of Pure and Applied Mathematics, 74(1):55–119, 2012.
|Date of creation||2013-03-22 19:31:25|
|Last modified on||2013-03-22 19:31:25|
|Last modified by||porton (9363)|