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

theorem Th52:
  IRRAT is dense Subset of R^1
proof
  Cl A = the carrier of R^1 by BORSUK_5:28;
  hence thesis by TOPS_3:def 2;
end;
