- #1
cappadonza
- 27
- 0
Hi this is more of a set theory question really, I'm a bit confused,
say [tex] \mathcal{F} [/tex] is collections of sets, and [tex] \mathcal{F}_n [/tex] is a sequence of sub collections of sets and say [tex] B_{1}, B_{2} ... [/tex] is a sequence of sets
what does the following mean [tex] \mathcal{S} = \{ A \in \mathcal{F} \colon A \cap B_{n} \in \mathcal{F}_n \forall n \in \mathbb{N} \} [/tex]
for an element to be a member of the set [tex] \mathcal{S} [/tex] which of the conditons must be statisfy
does this mean if [tex] A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{2} \in \mathcal{F}_2 ...[/tex] then it belongs to the set or
does it mean all these conditons must be met of it to be a members of the set [tex] A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{1} \in \mathcal{F}_2 , \space A \cap B_{1} \in \mathcal{F}_3 ... [/tex] for each [tex] B_{1}, B_{2} ...[/tex]
say [tex] \mathcal{F} [/tex] is collections of sets, and [tex] \mathcal{F}_n [/tex] is a sequence of sub collections of sets and say [tex] B_{1}, B_{2} ... [/tex] is a sequence of sets
what does the following mean [tex] \mathcal{S} = \{ A \in \mathcal{F} \colon A \cap B_{n} \in \mathcal{F}_n \forall n \in \mathbb{N} \} [/tex]
for an element to be a member of the set [tex] \mathcal{S} [/tex] which of the conditons must be statisfy
does this mean if [tex] A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{2} \in \mathcal{F}_2 ...[/tex] then it belongs to the set or
does it mean all these conditons must be met of it to be a members of the set [tex] A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{1} \in \mathcal{F}_2 , \space A \cap B_{1} \in \mathcal{F}_3 ... [/tex] for each [tex] B_{1}, B_{2} ...[/tex]