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 Th61:
  sigma TotFam T is all-open-containing compl-closed
  closed_for_countable_unions
proof
  set E = sigma TotFam T;
  TotFam T c= sigma TotFam T by PROB_1:def 9;
  hence E is all-open-containing;
  thus E is compl-closed;
  thus thesis;
end;
