reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T;
reserve x for Point of T;

theorem Th65:
  for F being open Subset-Family of T holds F c= BorelSets T
proof
  let F be open Subset-Family of T;
  F c= BorelSets T
  proof
    let x be object;
    assume
A1: x in F;
    then reconsider xx = x as Subset of T;
    xx is open by A1,TOPS_2:def 1;
    hence thesis by Def2;
  end;
  hence thesis;
end;
