Template:Families_of_sets
Template:Families of sets
Template's default state when transcluded is collapsed. To override, invoke as {{Families of sets|expanded}}
.
To change the template's position from the default shown, add the parameter position
with the value "left
", "center
", "centre
" or "right
".
Example call
Calling
{{Families of sets}}
will display:
Families of sets over | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Is necessarily true of or, is closed under: | Directed by | F.I.P. | ||||||||
π-system | ||||||||||
Semiring | Never | |||||||||
Semialgebra (Semifield) | Never | |||||||||
Monotone class | only if | only if | ||||||||
𝜆-system (Dynkin System) | only if | only if or they are disjoint | Never | |||||||
Ring (Order theory) | ||||||||||
Ring (Measure theory) | Never | |||||||||
δ-Ring | Never | |||||||||
𝜎-Ring | Never | |||||||||
Algebra (Field) | Never | |||||||||
𝜎-Algebra (𝜎-Field) | Never | |||||||||
Dual ideal | ||||||||||
Filter | Never | Never | ||||||||
Prefilter (Filter base) | Never | Never | ||||||||
Filter subbase | Never | Never | ||||||||
Open Topology | (even arbitrary ) | Never | ||||||||
Closed Topology | (even arbitrary ) | Never | ||||||||
Is necessarily true of or, is closed under: | directed downward | finite intersections | finite unions | relative complements | complements in | countable intersections | countable unions | contains | contains | Finite Intersection Property |
Additionally, a semiring is a π-system where every complement is equal to a finite disjoint union of sets in |
Call with alignment
Calling
{{Families of sets|position=left}}
will display:
Families of sets over | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Is necessarily true of or, is closed under: | Directed by | F.I.P. | ||||||||
π-system | ||||||||||
Semiring | Never | |||||||||
Semialgebra (Semifield) | Never | |||||||||
Monotone class | only if | only if | ||||||||
𝜆-system (Dynkin System) | only if | only if or they are disjoint | Never | |||||||
Ring (Order theory) | ||||||||||
Ring (Measure theory) | Never | |||||||||
δ-Ring | Never | |||||||||
𝜎-Ring | Never | |||||||||
Algebra (Field) | Never | |||||||||
𝜎-Algebra (𝜎-Field) | Never | |||||||||
Dual ideal | ||||||||||
Filter | Never | Never | ||||||||
Prefilter (Filter base) | Never | Never | ||||||||
Filter subbase | Never | Never | ||||||||
Open Topology | (even arbitrary ) | Never | ||||||||
Closed Topology | (even arbitrary ) | Never | ||||||||
Is necessarily true of or, is closed under: | directed downward | finite intersections | finite unions | relative complements | complements in | countable intersections | countable unions | contains | contains | Finite Intersection Property |
Additionally, a semiring is a π-system where every complement is equal to a finite disjoint union of sets in |
Expanded with alignment
Calling
{{Families of sets|expanded|position=left}}
will display:
Families of sets over | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Is necessarily true of or, is closed under: | Directed by | F.I.P. | ||||||||
π-system | ||||||||||
Semiring | Never | |||||||||
Semialgebra (Semifield) | Never | |||||||||
Monotone class | only if | only if | ||||||||
𝜆-system (Dynkin System) | only if | only if or they are disjoint | Never | |||||||
Ring (Order theory) | ||||||||||
Ring (Measure theory) | Never | |||||||||
δ-Ring | Never | |||||||||
𝜎-Ring | Never | |||||||||
Algebra (Field) | Never | |||||||||
𝜎-Algebra (𝜎-Field) | Never | |||||||||
Dual ideal | ||||||||||
Filter | Never | Never | ||||||||
Prefilter (Filter base) | Never | Never | ||||||||
Filter subbase | Never | Never | ||||||||
Open Topology | (even arbitrary ) | Never | ||||||||
Closed Topology | (even arbitrary ) | Never | ||||||||
Is necessarily true of or, is closed under: | directed downward | finite intersections | finite unions | relative complements | complements in | countable intersections | countable unions | contains | contains | Finite Intersection Property |
Additionally, a semiring is a π-system where every complement is equal to a finite disjoint union of sets in |
Editors can experiment in this template's sandbox (create | mirror) and testcases (create) pages.
Add categories to the /doc subpage. Subpages of this template.