A subset is said to be residual if there is such that whenever , and cofinal if for each there is such that .
A directed set is sometimes called an upward-directed set. We may also define the dual notion: a downward-directed set (or filtered set) is a partially ordered set such that whenever there is an such that and .
|Date of creation||2013-03-22 12:54:00|
|Last modified on||2013-03-22 12:54:00|
|Last modified by||yark (2760)|
|Synonym||upward directed set|
|Defines||downward directed set|