reserve T for TopSpace;
reserve T for non empty TopSpace;
reserve F for Subset-Family of T;
reserve T for non empty TopSpace;

theorem Th80:
  for F being Subset-Family of T holds F is open-domains-family
  implies F is open
proof
  let F be Subset-Family of T;
  assume
A1: F is open-domains-family;
  for A being Subset of T holds A in F implies A is open
  proof
    let A be Subset of T;
    assume A in F;
    then A is open_condensed by A1;
    hence thesis by TOPS_1:67;
  end;
  hence thesis by TOPS_2:def 1;
end;
