BabelNet

bn:01240237n

Noun Concept

Categories: Order theory, Articles with short description, General topology

filter Directed downward dual ideal Mathematical filter Normal filter

In mathematics, a filter or order filter is a special subset of a partially ordered set, describing "large" or "eventual" elements. Wikipedia

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In mathematics, a filter or order filter is a special subset of a partially ordered set, describing "large" or "eventual" elements. Wikipedia

A special subset of a partially ordered set. Wikipedia Disambiguation

A non-empty upper set (of a partially ordered set) which is closed under binary infima (a.k.a. meets). Wiktionary

The collection of cofinite subsets of ℝ is a filter under inclusion: it includes the intersection of every pair of its members, and includes every superset of every cofinite set. Wiktionary

If (1) the universal set (here, the set of natural numbers) were called a "large" set, (2) the superset of any "large" set were also a "large" set, and (3) the intersection of a pair of "large" sets were also a "large" set, then the set of all "large" sets would form a filter. Wiktionary

IS A

partially ordered set

HAS KIND

OPPOSITE OF

STUDIED BY

Wikipedia

filter (mathematics)

Wikidata