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

theorem Th13:
  for T being set, F being Subset-Family of T holds F is
  SigmaField of T iff F is compl-closed closed_for_countable_unions
proof
  let T be set, F be Subset-Family of T;
  thus F is SigmaField of T implies F is compl-closed
  closed_for_countable_unions;
  assume
A1: F is compl-closed closed_for_countable_unions;
  F is sigma-additive
  by A1;
  then reconsider
  F as non empty compl-closed sigma-additive Subset-Family of T by A1;
  F is SigmaField of T;
  hence thesis;
end;
