detials

Question number 7:
U := {A ⊂ E : complement of A ⊂ E}
We denote complement of A by Ac. In the question, it is denoted by CEA. We
will write it as Ac.
Now we will check that U is topology.
1. We have φ ⊂ E and E ⊂ E. Hence φ,E ∈ U .
2. Let {Aα} is collection from U . That is Aα ∈ U for each α....