f
filter
In order theory, a nonempty, downward‐directed, upward‐closed subset of a preordered set
EntityQ1052692
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Overview
All data
17 statements · 6% with external sources · numbers in brackets are citations
- Defining formula
\varnothing\ne \bigcup_{x\in F}\uparrow x=F\subset P\land(\forall x,y\in F\exists z\in F\colon x\ge z\le y)
- In defining formula
(P,\le)symbol represents: partially ordered set\varnothingsymbol represents: empty setFsymbol represents: filter\landsymbol represents: logical conjunction
On other databases
7 identifiers linking filter across the web's reference databases